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 A340403 #22 Jun 27 2023 11:27:04
%S A340403 3740,66914,1084508,16848674,256844060,3881598434,58426959068,
%T A340403 877826523554,13177356595100,197730071456354,2966439163566428,
%U A340403 44500004197580834,667523980478413340,10013027130697435874,150196578927865178588,2252956887698068132514
%N A340403 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 4) missing three edges, where the removed edges are incident to different vertices in the 4-point set and none of the removed edges are incident to the same vertex in the other set.
%C A340403 Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 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 the removed edges are incident to different points in A and none of the 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 A340403 Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries none of which are in the same row or column with no zero rows or columns.
%C A340403 Take a complete bipartite graph K(4,n) (with n at least 4) 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 three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.
%H A340403 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 A340403 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (26,-196,486,-315).
%F A340403 a(n) = 343*15^(n-3) - 216*7^(n-3) + 4*3^(n-1) - 1.
%F A340403 From _Stefano Spezia_, Jan 06 2021: (Start)
%F A340403 G.f.: 2*x^4*(1870 - 15163*x + 38892*x^2 - 25515*x^3)/(1 - 26*x + 196*x^2 - 486*x^3 + 315*x^4).
%F A340403 a(n) = 26*a(n-1) - 196*a(n-2) + 486*a(n-3) - 315*a(n-4) for n > 7. (End)
%t A340403 LinearRecurrence[{26,-196,486,-315},{3740,66914,1084508,16848674},20] (* _Harvey P. Dale_, Sep 18 2021 *)
%Y A340403 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 A340403 easy,nonn
%O A340403 4,1
%A A340403 _Rachel Wofford_, Jan 06 2021