A286191 a(n) = (2^n-1)^2 + 2*n.

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

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