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.
%I A340174 #41 Jun 27 2023 11:24:02
%S A340174 2792,140114,5366288,183405386,5953824632,188681559554,5911452093728,
%T A340174 184194287464826,5724142958302472,177660449252559794,
%U A340174 5510655708296433968,170878064308411409066,5297936128237164553112,164246762516365548788834,5091810779768636860563008
%N A340174 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 but are incident to the same vertex in the other set.
%C A340174 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 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'.
%C A340174 Number of {0,1} 5 X n matrices (with n at least 3) with two fixed zero entries in the same column and no zero rows or columns.
%C A340174 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 but are incident to the same vertex in B.
%H A340174 Steven Schlicker, Roman Vasquez, and Rachel Wofford, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Wofford/wofford4.html">Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
%H A340174 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (57,-1002,6562,-15381,9765).
%F A340174 a(n) = 7*31^(n-1) - 23*15^(n-1) + 4*7^n - 5*3^(n) + 3.
%F A340174 From _Alejandro J. Becerra Jr._, Feb 12 2021: (Start)
%F A340174 G.f.: 2*x^3*(126945*x^4 - 199953*x^3 + 88687*x^2 - 9515*x + 1396)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)).
%F A340174 a(n) = 57*a(n-1) - 1002*a(n-2) + 6562*a(n-3) - 15381*a(n-4) + 9765*a(n-5). (End)
%t A340174 Array[7*31^(# - 1) - 23*15^(# - 1) + 4*7^# - 5*3^(#) + 3 &, 15, 3] (* _Michael De Vlieger_, Jan 12 2021 *)
%t A340174 LinearRecurrence[{57,-1002,6562,-15381,9765},{2792,140114,5366288,183405386,5953824632},20] (* _Harvey P. Dale_, Aug 11 2021 *)
%Y A340174 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.
%Y A340174 Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
%Y A340174 Cf. A048291 (number of {0,1} n X n matrices with no zero rows or columns).
%K A340174 easy,nonn
%O A340174 3,1
%A A340174 _Steven Schlicker_, Dec 30 2020