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A210812
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Number of spanning trees in C_8 X P_n.
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2
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8, 150528, 1633023000, 16435095011328, 163038254770568232, 1612366324251306624000, 15934583650849932493684792, 157453155560517847607911907328, 1555776346581461837260983280509000, 15372327644619615416626608479388244992
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MAPLE
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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