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 A343800 #18 Jun 27 2023 11:53:11
%S A343800 978064,86336272,6348047008,430432446400,28099268578864,
%T A343800 1801251897183472,114448204851788608,7240412761411376800,
%U A343800 457083355837815526864,28825337854868779198672,1816898392511988031818208,114492570488330137017059200,7213899161676798784740778864
%N A343800 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 exactly two removed edges are incident to the same vertex in the 6-point set and exactly two removed edges are incident to the same vertex in the other set.
%C A343800 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 exactly two removed edges are incident to the same point in A and exactly two 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'.
%C A343800 Number of {0,1} 6 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns.
%C A343800 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 exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B.
%H A343800 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 A343800 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (120,-4593,69688,-428787,978768,-615195).
%F A343800 a(n) = 465*63^(n-2) - 1110*31^(n-2) + 967*15^(n-2) - 388*7^(n-2) + 70*3^(n-2) - 4.
%t A343800 Array[465*63^# - 1110*31^# + 967*15^# - 388*7^# + 70*3^# - 4 &[# - 2] &, 12, 4] (* _Michael De Vlieger_, May 01 2021 *)
%Y A343800 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.
%K A343800 easy,nonn
%O A343800 4,1
%A A343800 _Rachel Wofford_, Apr 29 2021