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 A340173 #32 Jul 22 2024 06:07:53
%S A340173 344,7568,133232,2145368,33235784,506005088,7642599392,115007387048,
%T A340173 1727691783224,25933450204208,389128287094352,5837810104155128,
%U A340173 87573352325069864,1313643690750940928,19704959203995442112,295576514963872161608
%N A340173 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(4,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 4-point set but are incident to the same vertex in the other set.
%C A340173 Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 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 A340173 Number of {0,1} 4 X n matrices (with n at least 3) with two fixed zero entries in the same column and no zero rows or columns.
%C A340173 Take a complete bipartite graph K(4,n) (with n at least 3) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,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 A340173 Paolo Xausa, <a href="/A340173/b340173.txt">Table of n, a(n) for n = 3..800</a>
%H A340173 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 A340173 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (26,-196,486,-315).
%F A340173 a(n) = 3*15^(n-1) - 8*7^(n-1) + 7*3^(n-1) - 2.
%F A340173 From _Stefano Spezia_, Dec 30 2020: (Start)
%F A340173 G.f.: 8*x^3*(43 - 172*x + 486*x^2 - 315*x^3)/(1 - 26*x + 196*x^2 - 486*x^3 + 315*x^4).
%F A340173 a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n > 6. (End)
%t A340173 A340173[n_] := 3*15^(n-1) - 8*7^(n-1) + 7*3^(n-1) - 2;
%t A340173 Array[A340173,25,3] (* _Paolo Xausa_, Jul 22 2024 *)
%Y A340173 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 A340173 Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939.
%Y A340173 Number of {0,1} n X n matrices with no zero rows or columns A048291.
%K A340173 easy,nonn
%O A340173 3,1
%A A340173 _Steven Schlicker_, Dec 30 2020