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 A340199 #19 Apr 10 2024 15:46:39
%S A340199 43,379,2899,21043,149563,1053739,7396579,51837283,363044683,
%T A340199 2541863899,17794700659,124567864723,871989933403,6103974174859,
%U A340199 42727953147139,299096073799363,2093673721903723,14655719669250619,102590048532528019
%N A340199 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 3-point set and are also not incident to the same vertex in the other set.
%C A340199 Start with a complete bipartite graph K(3,n) with vertex sets A and B where |A| = 3 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 and are also not 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 A340199 Number of {0,1} 3 X n matrices (with n at least 3) with two fixed zero entries not in the same row or column and no zero rows or columns.
%C A340199 Take a complete bipartite graph K(3,n) (with n at least 3) having parts A and B where |A| = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing two edges, where the two removed edges are not incident to the same vertex in A and are also not incident to the same vertex in B.
%H A340199 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 A340199 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-31,21).
%F A340199 a(n) = 9*7^(n-2) - 7*3^(n-2) + 1.
%F A340199 From _Stefano Spezia_, Dec 31 2020: (Start)
%F A340199 G.f.: x^3*(43 - 94*x + 63*x^2)/(1 - 11*x + 31*x^2 - 21*x^3).
%F A340199 a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n > 5. (End)
%t A340199 LinearRecurrence[{11,-31,21},{43,379,2899},20] (* _Harvey P. Dale_, Apr 10 2024 *)
%Y A340199 Other sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418. 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 A340199 easy,nonn
%O A340199 3,1
%A A340199 _Roman I. Vasquez_, Dec 31 2020