A210812 Number of spanning trees in C_8 X P_n.

8, 150528, 1633023000, 16435095011328, 163038254770568232, 1612366324251306624000, 15934583650849932493684792, 157453155560517847607911907328, 1555776346581461837260983280509000, 15372327644619615416626608479388244992

Offset: 1

Author

Alois P. Heinz, Mar 26 2012

Keywords

• nonn

Comments

A linear divisibility sequence. Factorizes as a product of second-order and fourth-order linear divisibility sequences. See Formula section. - Peter Bala, May 02 2014

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..50
• Index to divisibility sequences

Crossrefs

8th column of A173958.

Cf. A001109, A001353, A161158.

Programs

Maple

seq(expand(8*ChebyshevU(n-1,2)^2*ChebyshevU(n-1,3)*( ChebyshevU(n-1,(4+sqrt(2))/2)*ChebyshevU(n-1,(4-sqrt(2))/2) )^2), n = 1..10); # Peter Bala, May 02 2014

Formula

a(n) = 8*U(n-1,2)^2*U(n-1,3)*( U(n-1,(4+sqrt(2))/2)*U(n-1,(4-sqrt(2))/2) )^2 = 8*A001353(n)^2 * A001109(n) * A161158(n-1)^2, where U(n,x) is a Chebyshev polynomial of the second kind. - Peter Bala, May 02 2014