A158525 Number of connected spanning subgraphs and number of forests of the wheel graph W_n.

38, 134, 462, 1582, 5406, 18462, 63038, 215230, 734846, 2508926, 8566014, 29246206, 99852798, 340918782, 1163969534, 3974040574, 13568223230, 46324811774, 158162800638, 540001579006, 1843680714750, 6294719700990, 21491517374462, 73376630095870, 250523485634558

Offset

4,1

Comments

The wheel graph W_n has n vertices and 2n-2 edges. A single vertex is connected to all vertices of an (n-1)-cycle.

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..1000

Eric Weisstein's World of Mathematics, Wheel Graph

Wikipedia, Wheel graph

Index entries for linear recurrences with constant coefficients, signature (5,-6,2).

Formula

G.f.: (38-56*x+20*x^2)*x^4 / (6*x^2+1-5*x-2*x^3).

a(n) = 2 * A035344(n-2).

Maple

a:= n-> `if`(n<4, 0, (Matrix([[5, 1, 0], [ -6, 0, 1], [2, 0, 0]])^n)[3, 2]): seq(a(n), n=4..30);

Mathematica

CoefficientList[Series[((1 / x^4) (38 - 56 x + 20 x^2) x^4 / (6 x^2 + 1 - 5 x - 2 x^3)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)

Crossrefs

Cf. A035344.

Sequence in context: A044670 A118633 A216896 * A044370 A044751 A221403

Adjacent sequences: A158522 A158523 A158524 * A158526 A158527 A158528

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 20 2009

Status

approved