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%I A342328 #21 Jun 27 2023 11:44:18
%S A342328 1068475,89633839,6458329435,433976684431,28211055010555,
%T A342328 1804746233554159,114556965257054875,7243790885015626831,
%U A342328 457188176014823960635,28828588756092946562479,1816999192589895468925915,114495695622871975031439631
%N A342328 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 all three removed edges are incident to different vertices in the 6-point set but exactly two removed edges are incident to the same vertex in the other set.
%C A342328 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 all three removed edges are incident to different points in A but 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 A342328 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 column and no row has more than one zero entry, with no zero rows or columns.
%C A342328 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 all three removed edges are incident to different vertices in A but exactly two removed edges are incident to the same vertex in B.
%H A342328 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 A342328 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (120,-4593,69688,-428787,978768,-615195).
%F A342328 a(n) = 465*63^(n-2) - 982*31^(n-2) + 807*15^(n-2) - 316*7^(n-2) + 56*3^(n-2) - 3.
%t A342328 Array[465*63^(# - 2) - 982*31^(# - 2) + 807*15^(# - 2) - 316*7^(# - 2) + 56*3^(# - 2) - 3 &, 12, 4] (* _Michael De Vlieger_, Mar 19 2021 *)
%Y A342328 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 A342328 easy,nonn
%O A342328 4,1
%A A342328 _Steven Schlicker_, Mar 08 2021

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