cp's OEIS Frontend

A342580 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 4) missing three edges, where all three removed edges are incident to the same vertex in the 5-point set.

%I A342580 #45 Jun 27 2023 15:46:16
%S A342580 43664,2248976,85045184,2880236192,93044373104,2941433979056,
%T A342580 92045266123424,2866350051682112,89051296064477264,
%U A342580 2763508542463136336,85712552167491668864,2657746010652834993632,82399980314514994098224,2554547203590738451564016
%N A342580 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 4) missing three edges, where all three removed edges are incident to the same vertex in the 5-point set.
%C A342580 Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 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 the same point in A. So this sequence tells the number of sets at each location on the line segment between A' and B'.
%C A342580 Number of {0,1} 5 X n matrices (with n at least 4) with three fixed zero entries all in the same row and no zero rows or columns.
%C A342580 Take a complete bipartite graph K(5,n) (with n at least 4) 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 three edges, where all three removed edges are incident same vertex in A.
%H A342580 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 A342580 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (57,-1002,6562,-15381,9765).
%F A342580 a(n) = 3375*31^(n-3) - 4747*15^(n-3) - 166*3^(n-3) + 1534*7^(n-3) + 4.
%Y A342580 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 A342580 Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
%Y A342580 Number of {0,1} n X n matrices with no zero rows or columns A048291.
%K A342580 easy,nonn
%O A342580 4,1
%A A342580 _Roman I. Vasquez_, Mar 24 2021