cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 35 results. Next

A335608 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 2) missing one edge.

Original entry on oeis.org

8, 104, 896, 6800, 49208, 349304, 2459696, 17261600, 120962408, 847130504, 5931094496, 41521204400, 290659059608, 2034645303704, 14242612785296, 99698576475200, 697890896260808, 4885238856628904, 34196679744812096, 239376781458914000, 1675637539948086008
Offset: 2

Views

Author

Steven Schlicker, Jun 15 2020

Keywords

Comments

Number of {0,1} 3 X n matrices with one fixed zero entry and no zero rows or columns.
Number of edge covers of a complete bipartite graph K(3,n) (with n at least 2) missing one edge.

Examples

			For n = 2, a(2) = 8.
		

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

  • Mathematica
    Array[3*7^(# - 1) - 5*3^(# - 1) + 2 &, 21, 2] (* Michael De Vlieger, Jun 22 2020 *)

Formula

a(n) = 3*7^(n-1) - 5*3^(n-1) + 2.
From Stefano Spezia, Jul 04 2020: (Start)
G.f.: x^2*(8 + 16*x)/(1 - 11*x + 31*x^2 - 21*x^3).
a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n > 4. (End)

A335613 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the removed edges are incident to the same vertex in the four point part.

Original entry on oeis.org

290, 7568, 140114, 2300576, 35939330, 549221168, 8309585714, 125143712576, 1880658325730, 28234402793168, 423687765591314, 6356518634756576, 95356194832648130, 1430401830434093168, 21456439814417820914, 321849483728499752576, 4827762461533785786530
Offset: 3

Views

Author

Steven Schlicker, Jul 16 2020

Keywords

Comments

The Hausdorff metric defines a distance between sets. Using this distance we can define line segments with sets as endpoints. Create two sets from the vertices of the parts A and B (with |A| = 4) of a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the removed edges are incident to the same point in A. Points in the sets A and B that correspond to vertices that are connected by edges are the same Euclidean distance apart. This sequence tells the number of sets at each location on the line segment between A and B.
Number of {0,1} 4 X n (with n at least 3) matrices with two fixed zero entries in the same row and no zero rows or columns.
Take a complete bipartite graph K(4,n) (with n at least 3) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing two edges, where the two removed edges are incident to the same vertex in A.

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

  • Maple
    a:= proc(n) 49*15^(n-2)-76*7^(n-2)+10*3^(n-1)-3 end proc: seq(a(n), n=3..20);
  • PARI
    Vec(2*x^3*(145 + 14*x + 93*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)) + O(x^22)) \\ Colin Barker, Jul 17 2020

Formula

a(n) = 49*15^(n-2) - 76*7^(n-2) + 10*3^(n-1) - 3.
From Colin Barker, Jul 17 2020: (Start)
G.f.: 2*x^3*(145 + 14*x + 93*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)).
a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n>6.
(End)

A337416 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(5,n) (with n at least 3) missing two edges, where the removed edges are incident to the same point in the 5 point part.

Original entry on oeis.org

2240, 133232, 5366288, 187074656, 6126049760, 194922245072, 6118612137008, 190822947290816, 5932740419114240, 184173665371614512, 5713266248795701328, 177169506604462719776, 5493128593023515417120, 170300095372377973419152, 5279499596024093537691248
Offset: 3

Views

Author

Steven Schlicker, Aug 26 2020

Keywords

Comments

The Hausdorff metric defines a distance between sets. Using this distance we can define line segments with sets as endpoints. Create two sets from the vertices of the parts A and B (with |A| = 5) of a complete bipartite graph K(5,n) (with n at least 3) missing two edges, where the removed edges are incident to the same point in A. Points in the sets A and B that correspond to vertices that are connected by edges are the same Euclidean distance apart. This sequence tells the number of sets at each location on the line segment between A and B.
Number of {0,1} 5 X n (with n at least 3) matrices with two fixed zero entries in the same row and no zero rows or columns.
Take a complete bipartite graph K(5,n) (with n at least 3) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K_{5,n} graph after removing two edges, where the two removed edges are incident to the same vertex in A.

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

  • Maple
    a:= proc(n) 225*31^(n-2) - 421*15^(n-2)+250*7^(n-2)-58*3^(n-2)+4 end proc: seq(a(n), n=3..20);

Formula

a(n) = 225*31^(n-2) - 421*15^(n-2) + 250*7^(n-2) - 58*3^(n-2) + 4.
From Colin Barker, Oct 13 2020: (Start)
G.f.: 16*x^3*(140 + 347*x + 1034*x^2 - 261*x^3) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)).
a(n) = 57*a(n-1) - 1002*a(n-2) + 6562*a(n-3) - 15381*a(n-4) + 9765*a(n-5) for n>7.
(End)

A337418 Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are not incident to the same vertex in the 3 point part but are incident to the same vertex in the other part.

Original entry on oeis.org

32, 290, 2240, 16322, 116192, 819170, 5751680, 40314242, 282357152, 1976972450, 13840224320, 96885821762, 678213506912, 4747532812130, 33232844476160, 232630255706882, 1628412823069472, 11398892860850210, 79792259324043200, 558545843162577602
Offset: 3

Views

Author

Steven Schlicker, Aug 26 2020

Keywords

Comments

The Hausdorff metric defines a distance between sets. Using this distance we can define line segments with sets as endpoints. Create two sets from the vertices of the parts A and B (with |A| = 3) of a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are not incident to the same vertex in A but are incident to the same vertex in B. Points in the sets A and B that correspond to vertices that are connected by edges are the same Euclidean distance apart. This sequence tells the number of sets at each location on the line segment between A and B.
Number of {0,1} 3 X n (with n at least 3) matrices with two fixed zero entries in the same column and no zero rows or columns.
Take a complete bipartite graph K(3,n) (with n at least 3) having parts A and B where |A| = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing two edges, where the removed edges are not incident to the same vertex in A but are incident to the same vertex in B.

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

  • Maple
    a:= proc(n) 7^(n-1)-2*3^(n-1)+1 end proc: seq(a(n), n=3..20);
  • Mathematica
    A337418[n_] := 7^(n-1) - 2*3^(n-1) + 1;
    Array[A337418,25,3] (* Paolo Xausa, Jul 22 2024 *)
  • PARI
    Vec(2*x^3*(16 - 31*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)) + O(x^25)) \\ Colin Barker, Nov 20 2020

Formula

a(n) = 7^(n-1)-2*3^(n-1)+1.
From Colin Barker, Nov 20 2020: (Start)
G.f.: 2*x^3*(16 - 31*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)).
a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n>5. (End)

A340173 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 4-point set but are incident to the same vertex in the other set.

Original entry on oeis.org

344, 7568, 133232, 2145368, 33235784, 506005088, 7642599392, 115007387048, 1727691783224, 25933450204208, 389128287094352, 5837810104155128, 87573352325069864, 1313643690750940928, 19704959203995442112, 295576514963872161608
Offset: 3

Views

Author

Steven Schlicker, Dec 30 2020

Keywords

Comments

Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 3. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing two edges, where the two removed edges are not incident to the same point in A but are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 4 X n matrices (with n at least 3) with two fixed zero entries in the same column and no zero rows or columns.
Take a complete bipartite graph K(4,n) (with n at least 3) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing two edges, where the two removed edges are not incident to the same vertex in A but are incident to the same vertex in B.

Crossrefs

Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

Formula

a(n) = 3*15^(n-1) - 8*7^(n-1) + 7*3^(n-1) - 2.
From Stefano Spezia, Dec 30 2020: (Start)
G.f.: 8*x^3*(43 - 172*x + 486*x^2 - 315*x^3)/(1 - 26*x + 196*x^2 - 486*x^3 + 315*x^4).
a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n > 6. (End)

A340175 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(6,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 6-point set but are incident to the same vertex in the other set.

Original entry on oeis.org

20720, 2300576, 187074656, 13292505200, 887383104080, 57504128509376, 3673096729270976, 232977132982939280, 14726467240259960240, 929286203862118743776, 58592152032205560862496, 3692766925932013206557360, 232689626985868508845398800
Offset: 3

Views

Author

Steven Schlicker, Dec 30 2020

Keywords

Comments

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 3. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing two edges, where the two removed edges are not incident to the same point in A but are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 6 X n matrices (with n at least 3) with two fixed zero entries in the same column and no zero rows or columns.
Take a complete bipartite graph K(6,n) (with n at least 3) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing two edges, where the two removed edges are not incident to the same vertex in A but are incident to the same vertex in B.

Crossrefs

Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

  • Mathematica
    A340175[n_] := 15*63^(n-1) - 58*31^(n-1) + 89*15^(n-1) - 68*7^(n-1) + 26*3^(n-1) - 4; Array[A340175, 20, 3] (* or *)
    LinearRecurrence[{120, -4593, 69688, -428787, 978768, -615195}, {20720, 2300576, 187074656, 13292505200, 887383104080, 57504128509376}, 20] (* Paolo Xausa, Jul 22 2024 *)

Formula

a(n) = 15*63^(n-1) - 58*31^(n-1) + 89*15^(n-1) - 68*7^(n-1) + 26*3^(n-1) - 4.
From Alejandro J. Becerra Jr., Feb 12 2021: (Start)
G.f.: -16*x^3*(3075975*x^5 - 4893840*x^4 + 2115207*x^3 - 385781*x^2 + 11614*x - 1295)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)*(1 - 63*x)).
a(n) = 120*a(n-1) - 4593*a(n-2) + 69688*a(n-3) - 428787*a(n-4) + 978768*a(n-5) - 615195*a(n-6). (End)

A340201 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(5,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 5-point set and are also not incident to the same vertex in the other set.

Original entry on oeis.org

2899, 145387, 5566147, 190200379, 6173845939, 195645606667, 6129507633187, 190986695659099, 5935198857377299, 184210557438511147, 5713819738261143427, 177177809705712311419, 5493253144857237049459, 170301963687088948318027, 5279527621005195132400867
Offset: 3

Views

Author

Roman I. Vasquez, Dec 31 2020

Keywords

Comments

Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 and |B| is at least 3. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing two edges, where the two removed edges are not incident to the same point in A and are also not incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 5 X n matrices (with n at least 3) with two fixed zero entries not in the same row or column and no zero rows or columns.
Take a complete bipartite graph K(5,n) (with n at least 3) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K(5,n) graph after removing two edges, where the two removed edges are not incident to the same vertex in A and are also not incident to the same vertex in B.

Crossrefs

Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
Number of {0,1} n X n matrices with no zero rows or columns A048291.

Formula

a(n) = 225*31^(n-2) - 357*15^(n-2) + 202*7^(n-2) - 46*3^(n-2) + 3.
From Alejandro J. Becerra Jr., Feb 14 2021: (Start)
G.f.: x^3*(263655*x^4 - 415464*x^3 + 183886*x^2 - 19856*x + 2899)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)).
a(n) = 57*a(n-1) - 1002*a(n-2) + 6562*a(n-3) - 15381*a(a-4) + 9765*a(n-5). (End)

A340403 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 4) missing three edges, where the removed edges are incident to different vertices in the 4-point set and none of the removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

3740, 66914, 1084508, 16848674, 256844060, 3881598434, 58426959068, 877826523554, 13177356595100, 197730071456354, 2966439163566428, 44500004197580834, 667523980478413340, 10013027130697435874, 150196578927865178588, 2252956887698068132514
Offset: 4

Views

Author

Rachel Wofford, Jan 06 2021

Keywords

Comments

Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where the removed edges are incident to different points in A and none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries none of which are in the same row or column with no zero rows or columns.
Take a complete bipartite graph K(4,n) (with n at least 4) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Programs

  • Mathematica
    LinearRecurrence[{26,-196,486,-315},{3740,66914,1084508,16848674},20] (* Harvey P. Dale, Sep 18 2021 *)

Formula

a(n) = 343*15^(n-3) - 216*7^(n-3) + 4*3^(n-1) - 1.
From Stefano Spezia, Jan 06 2021: (Start)
G.f.: 2*x^4*(1870 - 15163*x + 38892*x^2 - 25515*x^3)/(1 - 26*x + 196*x^2 - 486*x^3 + 315*x^4).
a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n > 7. (End)

A340405 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(6,n) (with n at least 4) missing three edges, where the removed edges are incident to different vertices in the 6-point set and none of the removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

1084508, 91075250, 6565114436, 441241902314, 28686096681068, 1835221289891810, 116494017052053716, 7366358270603987354, 464926482693459729788, 29316615999089974986770, 1847760848280105290960996, 116434174169077299044440394, 7336135517363636128979098508
Offset: 4

Views

Author

Rachel Wofford, Jan 06 2021

Keywords

Comments

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where the removed edges are incident to different points in A and none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 6 X n matrices with three fixed zero entries none of which are in the same row or column with no zero rows or columns.
Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Formula

a(n) = 29791*63^(n-3) - 31050*31^(n-3) + 12369*15^(n-3) - 2260*7^(n-3) + 19*3^(n-1) - 3.
From Alejandro J. Becerra Jr., Feb 13 2021: (Start)
G.f.: -2*x^4*(2773914255*x^5 - 4404958866*x^4 + 1920200130*x^3 - 308614840*x^2 + 19532855*x - 542254)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)*(1 - 63*x)).
a(n) = 120*a(n-1) - 4593*a(n-2) + 69688*a(n-3) - 428787*a(n-4) + 978768*a(n-5) - 615195*a(n-6). (End)

A340433 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 4-point set but all three removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

2426, 43664, 709682, 11039864, 168395306, 2545615904, 38322357602, 575803142024, 8643824410586, 129704815623344, 1945904406111122, 29190891370520984, 437879647739376266, 6568308657050321984, 98525427444538818242, 1477886994795768920744
Offset: 4

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Author

Rachel Wofford, Jan 07 2021

Keywords

Comments

Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where all three removed edges are incident to different points in A but all three removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries all of which are in the same column with no zero rows or columns.
Take a complete bipartite graph K(4,n) (with n at least 4) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Crossrefs

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Formula

a(n) = 15^(n-1) - 3*7^(n-1) + 3^(n) - 1.
From Stefano Spezia, Jan 07 2021: (Start)
G.f.: 2*x^4*(1213 - 9706*x + 24957*x^2 - 16380*x^3)/(1 - 26*x + 196*x^2 - 486*x^3 + 315*x^4).
a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n > 7. (End)
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