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 A286191 a(n) = (2^n-1)^2 + 2*n. 3
 3, 13, 55, 233, 971, 3981, 16143, 65041, 261139, 1046549, 4190231, 16769049, 67092507, 268402717, 1073676319, 4294836257, 17179607075, 68718952485, 274876858407, 1099509530665, 4398042316843, 17592177655853, 70368727400495, 281474943156273, 1125899839733811 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Number of connected induced (non-null) subgraphs of the complete bipartite graph K(n,n). LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Complete Bipartite Graph Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph Index entries for linear recurrences with constant coefficients, signature (8,-21,22,-8). FORMULA a(n) = (2^n-1)^2 + 2*n. From Colin Barker, May 30 2017: (Start) G.f.: x*(3 - 11*x + 14*x^2) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)). a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4) for n>4. (End) MATHEMATICA a[n_] := (2^n-1)^2 + 2*n; Array[a, 30] Table[(2^n - 1)^2 + 2 n, {n, 20}] (* Eric W. Weisstein, Aug 09 2017 *) LinearRecurrence[{8, -21, 22, -8}, {3, 13, 55, 233}, 20] (* Eric W. Weisstein, Aug 09 2017 *) CoefficientList[Series[(3 - 11 x + 14 x^2)/((-1 + x)^2 (1 - 6 x + 8 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 09 2017 *) PROG (PARI) Vec(x*(3 - 11*x + 14*x^2) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, May 30 2017 CROSSREFS Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook),  A285765 (queen). Sequence in context: A302757 A093834 A296045 * A033887 A291653 A183804 Adjacent sequences:  A286188 A286189 A286190 * A286192 A286193 A286194 KEYWORD nonn,easy AUTHOR Giovanni Resta, May 05 2017 EXTENSIONS Name changed to the formula by Eric W. Weisstein, Aug 09 2017 STATUS approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)