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A210813
Number of spanning trees in C_10 X P_n.
2
10, 2620860, 321437558750, 34966152200584440, 3696387867279360000000, 387686455761449000565832500, 40568852698294278820875719309510, 4242420895960521871557351517779467760, 443556393051604632125747307341249759676250
OFFSET
1,1
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
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)
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
CROSSREFS
10th column of A173958.
Sequence in context: A069878 A235029 A013854 * A116126 A220145 A057141
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 26 2012
STATUS
approved