A003756 Number of spanning trees with degrees 1 and 3 in S_4 X P_{2n-1}.

1, 0, 24, 54, 492, 1944, 11976, 57024, 313440, 1587168, 8417472, 43483392, 227995008, 1185394176, 6192642048, 32263570944, 168350991360, 877689686016, 4578049517568, 23872537976832, 124504626978816, 649282059657216, 3386128302882816, 17658788068196352

Offset

1,3

References

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Links

Table of n, a(n) for n=1..24.

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs

F. Faase, Results from the counting program

Index entries for sequences related to trees

Index entries for linear recurrences with constant coefficients, signature (2, 16, 4).

Formula

a(n) = 2*a(n-1) + 16*a(n-2) + 4*a(n-3), n > 4.

G.f.: x*(1 + 8*x^2 + 2*x^3 - 2*x)/(1 - 2*x - 16*x^2 - 4*x^3). - R. J. Mathar, Dec 16 2008

Mathematica

Join[{1, 0}, LinearRecurrence[{2, 16, 4}, {24, 54, 492}, 20]] (* Harvey P. Dale, Mar 17 2013 *)

Crossrefs

Sequence in context: A005782 A351379 A038635 * A135191 A216697 A332541

Adjacent sequences: A003753 A003754 A003755 * A003757 A003758 A003759

Keyword

nonn,easy

Author

Frans J. Faase; corrections Feb 07 2009

Status

approved