A210813 Number of spanning trees in C_10 X P_n.

10, 2620860, 321437558750, 34966152200584440, 3696387867279360000000, 387686455761449000565832500, 40568852698294278820875719309510, 4242420895960521871557351517779467760, 443556393051604632125747307341249759676250

Offset: 1

Author

Alois P. Heinz, Mar 26 2012

Keywords

• nonn
• easy

Comments

A linear divisibility sequence: Factorizes as a product of second-order and fourth-order linear divisibility sequences. See the 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

10th column of A173958.

Cf. A001109, A003733, A143699, A241606.

Programs

Maple

seq(expand(10*ChebyshevU(n-1,3)*( ChebyshevU(n-1,(7 + sqrt(5))/4)*ChebyshevU(n-1,(7 - sqrt(5))/4) )^2 * ( ChebyshevU(n-1,(9 + sqrt(5))/4)*ChebyshevU(n-1,(9 - sqrt(5))/4) )^2), n = 1..10); # Peter Bala, May 02 2014

Formula

From Peter Bala, May 02 2014: (Start)

a(n) = 10*U(n-1,3)*( U(n-1,(7 + sqrt(5))/4)*U(n-1,(7 - sqrt(5))/4) )^2 * ( U(n-1,(9 + sqrt(5))/4)*U(n-1,(9 - sqrt(5))/4) )^2, where U(n,x) is a Chebyshev polynomial of the second kind,

a(n) = 10*A001109(n) * A241606(n)^2 * A143699(n)^2 = 2*A001109(n) * A241606(n)^2 * A003733(n). (End)