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.

Previous Showing 11-20 of 20 results.

A079921 Solution to the Dancing School Problem with n girls and n+2 boys: f(n,2).

Original entry on oeis.org

3, 7, 14, 26, 46, 79, 133, 221, 364, 596, 972, 1581, 2567, 4163, 6746, 10926, 17690, 28635, 46345, 75001, 121368, 196392, 317784, 514201, 832011, 1346239, 2178278, 3524546, 5702854, 9227431, 14930317, 24157781, 39088132, 63245948, 102334116, 165580101
Offset: 1

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
With offset 4, number of 132-avoiding two-stack sortable permutations which contain exactly one subsequence of type 123.

Links

Crossrefs

Cf. A000045, A079908-A079928, A001924.
Cf. Essentially the same as A001924.

Programs

  • Maple
    with(genfunc): Fz := 1/((-1+z)^2 * (1-z-z^2)); seq(rgf_term(Fz,z,n), n=1..30);
  • Mathematica
    CoefficientList[Series[(-z^3 + z^2 + 2*z - 3)/((z - 1)^2 (z^2 + z - 1)), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
LinearRecurrence[{3,-2,-1,1},{3,7,14,26},40] (* Harvey P. Dale, Oct 17 2022 *)

Formula

a(n) = a(n-1)+a(n-2)+n+1, a(1)=3, a(2)=7.
G.f.: 1/((1-x)^2*(1-x-x^2)).
F(n+5) - n - 4, F(n) = A000045(n).
a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). - Wesley Ivan Hurt, Dec 03 2021

Extensions

More terms from Jaap Spies, Dec 15 2006

A079922 Solution to the Dancing School Problem with n girls and n+3 boys: f(n,3).

Original entry on oeis.org

4, 13, 36, 90, 212, 478, 1044, 2227, 4664, 9627, 19640, 39684, 79544, 158364, 313464, 617365, 1210588, 2364713, 4603388, 8934142, 17291756, 33385018, 64311660, 123634471, 237233712, 454429239, 869095472, 1659708488
Offset: 1

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.

Links

Crossrefs

Cf. A079908-A079928.

Formula

Empirical g.f.: -x*(x^7-4*x^4+2*x^3+3*x-4) / ((x-1)^2*(x^3+x^2+x-1)^2). - Colin Barker, Jan 04 2015

Extensions

More terms from Jaap Spies, Dec 15 2006

A079923 Solution to the Dancing School Problem with n girls and n+4 boys: f(n,4).

Original entry on oeis.org

5, 21, 76, 246, 738, 2108, 5794, 15458, 40296, 103129, 260019, 647617, 1596800, 3904260, 9479292, 22879520, 54947836, 131406732, 313129592, 743878505, 1762572329, 4167010597, 9832766588, 23164353834
Offset: 1

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.

Links

Crossrefs

Cf. A079908-A079928.

Extensions

More terms from Jaap Spies, Dec 14 2006

A079924 Solution to the Dancing School Problem with n girls and n+5 boys: f(n,5).

Original entry on oeis.org

6, 31, 140, 566, 2104, 7364, 24720, 80196, 253072, 780902, 2365772, 7058469, 20789082, 60560175, 174763208, 500245052, 1421824896, 4016278792, 11283371280, 31547434008, 87827653936, 243578509132, 673221043496
Offset: 1

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.

References

  • Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.

Links

Crossrefs

Cf. A079908-A079928.

Extensions

More terms from Jaap Spies, Dec 14 2006

A079925 Solution to the Dancing School Problem with n girls and n+6 boys: f(n,6).

Original entry on oeis.org

7, 43, 234, 1146, 5150, 21652, 86608, 334072, 1249768, 4557284, 16266830, 57031078, 196933710, 671224467, 2262089361, 7548882573, 24975936372, 82012110724, 267505920876, 867390073384
Offset: 1

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.

Links

Crossrefs

Cf. A079908-A079928.

Extensions

Corrected by Jaap Spies, Feb 01 2004
More terms Dec 14 2006

A079927 Solution to the Dancing School Problem with n girls and n+8 boys: f(n,8).

Original entry on oeis.org

9, 73, 536, 3590, 22162, 127604, 693552, 3598120, 17990600, 87396728, 413977192, 1918222840, 8719846960, 38983643908, 171764779170, 747190081890, 3213760467348, 13684132415133, 57742830924831, 241687792906641
Offset: 1

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.

Links

Crossrefs

Cf. A079908-A079928.

Extensions

Corrected by Jaap Spies, Feb 01 2004
More terms Dec 14 2006

A079916 Solution to the Dancing School Problem with 11 girls and n+11 boys: f(11,n).

Original entry on oeis.org

1, 12, 972, 19640, 260019, 2365772, 16266830, 89700624, 413977192, 1650607040, 5826331440, 18558391936, 54055214144, 145576033920, 365883104080, 865023114560, 1936764883296, 4130528893504, 8433028861040
Offset: 0

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.

Links

Crossrefs

Cf. A079908-A079928.

Extensions

Corrected by Jaap Spies, Feb 01 2004

A079917 Solution to the Dancing School Problem with 12 girls and n+12 boys: f(12,n).

Original entry on oeis.org

1, 13, 1581, 39684, 647617, 7058469, 57031078, 363862092, 1918222840, 8641355080, 34132685120, 120629547584, 387665694976, 1145875468544, 3145428883520
Offset: 0

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.

Links

Crossrefs

Cf. A079908-A079928.

Extensions

Corrected by Jaap Spies, Feb 01 2004

A079919 Solution to the Dancing School Problem with 14 girls and n+14 boys: f(14,n).

Original entry on oeis.org

1, 15, 4163, 158364, 3904260, 60560175, 671224467, 5697401802, 38983643908, 223245029176, 1100925116264, 4780871048064, 18612106195456, 65909241461760, 214868401724416, 650515953570304, 1842743223078144, 4916155345428736, 12422627638293760, 29881211844270336, 68721268507385344, 151698799246127104
Offset: 0

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.

Links

Crossrefs

Cf. A079908-A079928.

Formula

a(n) = n^14 - 77*n^13 + 3094*n^12 - 83083*n^11 + 1637636*n^10 - 24785761*n^9 + 294696402*n^8 - 2779448529*n^7 + 20797459683*n^6 - 122389753486*n^5 + 555826054784*n^4 - 1883902028008*n^3 + 4494445040176*n^2 - 6742111050752*n + 4789534153984 for n >= 12. - Georg Fischer, Apr 27 2021 (polynomial computed by the program in links)

Extensions

Corrected by Jaap Spies, Feb 01 2004
a(13)-a(21) from Georg Fischer, Apr 27 2021

A079920 Solution to the Dancing School Problem with 15 girls and n+15 boys: f(15,n).

Original entry on oeis.org

1, 16, 6746, 313464, 9479292, 174763208, 2262089361, 22088730348, 171764779170, 1106667645872, 6087616677864, 29267369636800, 125299076209408, 485013257865472, 1718947213795328, 5636819806209792, 17235204961273600, 49467590616190208, 134058587073795072, 344809293460572928, 845577589114049792, 1985060631106310400
Offset: 0

Views

Author

Jaap Spies, Jan 28 2003

Keywords

Comments

f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.

Links

Crossrefs

Cf. A079908-A079928.

Formula

a(n) = n^15 - 90*n^14 + 4200*n^13 - 131040*n^12 + 3011190*n^11 - 53441388*n^10 + 751250500*n^9 - 8470570680*n^8 + 76896261585*n^7 - 560015385930*n^6 + 3235452199980*n^5 - 14525684311320*n^4 + 48947506506080*n^3 - 116650912956480*n^2 + 175512302620800*n - 125495209214208 for n >= 13. - Georg Fischer, Apr 27 2021 (polynomial computed by the program in links)

Extensions

Corrected by Jaap Spies, Feb 01 2004
a(12)-a(21) from Georg Fischer, Apr 27 2021
Previous Showing 11-20 of 20 results.

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