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 A340201 #24 Jun 27 2023 11:27:07
%S A340201 2899,145387,5566147,190200379,6173845939,195645606667,6129507633187,
%T A340201 190986695659099,5935198857377299,184210557438511147,
%U A340201 5713819738261143427,177177809705712311419,5493253144857237049459,170301963687088948318027,5279527621005195132400867
%N 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.
%C A340201 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'.
%C A340201 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.
%C A340201 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.
%H A340201 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 A340201 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (57,-1002,6562,-15381,9765).
%F A340201 a(n) = 225*31^(n-2) - 357*15^(n-2) + 202*7^(n-2) - 46*3^(n-2) + 3.
%F A340201 From _Alejandro J. Becerra Jr._, Feb 14 2021: (Start)
%F A340201 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)).
%F A340201 a(n) = 57*a(n-1) - 1002*a(n-2) + 6562*a(n-3) - 15381*a(a-4) + 9765*a(n-5). (End)
%Y A340201 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 A340201 Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
%Y A340201 Number of {0,1} n X n matrices with no zero rows or columns A048291.
%K A340201 easy,nonn
%O A340201 3,1
%A A340201 _Roman I. Vasquez_, Dec 31 2020