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 A337418 #37 Jul 22 2024 05:57:50
%S A337418 32,290,2240,16322,116192,819170,5751680,40314242,282357152,
%T A337418 1976972450,13840224320,96885821762,678213506912,4747532812130,
%U A337418 33232844476160,232630255706882,1628412823069472,11398892860850210,79792259324043200,558545843162577602
%N A337418 Number of sets (in the Hausdorff metric geometry) 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 removed edges are not incident to the same vertex in the 3 point part but are incident to the same vertex in the other part.
%C A337418 The Hausdorff metric defines a distance between sets. Using this distance we can define line segments with sets as endpoints. Create two sets from the vertices of the parts A and B (with |A| = 3) of a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are not incident to the same vertex in A but are incident to the same vertex in B. Points in the sets A and B that correspond to vertices that are connected by edges are the same Euclidean distance apart. This sequence tells the number of sets at each location on the line segment between A and B.
%C A337418 Number of {0,1} 3 X n (with n at least 3) matrices with two fixed zero entries in the same column and no zero rows or columns.
%C A337418 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 removed edges are not incident to the same vertex in A but are incident to the same vertex in B.
%H A337418 Paolo Xausa, <a href="/A337418/b337418.txt">Table of n, a(n) for n = 3..1000</a>
%H A337418 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 A337418 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-31,21).
%F A337418 a(n) = 7^(n-1)-2*3^(n-1)+1.
%F A337418 From _Colin Barker_, Nov 20 2020: (Start)
%F A337418 G.f.: 2*x^3*(16 - 31*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)).
%F A337418 a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) for n>5. (End)
%p A337418 a:= proc(n) 7^(n-1)-2*3^(n-1)+1 end proc: seq(a(n), n=3..20);
%t A337418 A337418[n_] := 7^(n-1) - 2*3^(n-1) + 1;
%t A337418 Array[A337418,25,3] (* _Paolo Xausa_, Jul 22 2024 *)
%o A337418 (PARI) Vec(2*x^3*(16 - 31*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)) + O(x^25)) \\ _Colin Barker_, Nov 20 2020
%Y A337418 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 A337418 easy,nonn
%O A337418 3,1
%A A337418 _Steven Schlicker_, Aug 26 2020