A003691 Number of spanning trees with degrees 1 and 3 in K_3 X P_2n.

3, 36, 324, 2880, 25632, 228096, 2029824, 18063360, 160745472, 1430470656, 12729729024, 113281597440, 1008090611712, 8970977673216, 79832546279424, 710428191621120

Offset

1,1

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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 (8,8).

Formula

a(n) = 8*a(n-1) + 8*a(n-2), n>3.

From Bruno Berselli, Aug 02 2011: (Start)

G.f.: 3*x*(1+2*x)^2/(1-8*x-8*x^2).

For n>1, a(n) = 3*sqrt(3)*sqrt(2^(2*n-7))*((2+sqrt(6))^n-(2-sqrt(6))^n). (End)

Prog

(Magma) i:=[3, 36, 324]; [n le 3 select i[n] else 8*(Self(n-1)+Self(n-2)): n in [1..16]];  // Bruno Berselli, Aug 02 2011
(PARI) a(n)=([0, 1; 8, 8]^(n-1)*[3; 36])[1, 1] \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Cf. A057091.

Sequence in context: A073980 A034860 A220831 * A038146 A067444 A092648

Adjacent sequences: A003688 A003689 A003690 * A003692 A003693 A003694

Keyword

nonn,easy

Author

Frans J. Faase

Status

approved