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A210813
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Number of spanning trees in C_10 X P_n.
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2
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10, 2620860, 321437558750, 34966152200584440, 3696387867279360000000, 387686455761449000565832500, 40568852698294278820875719309510, 4242420895960521871557351517779467760, 443556393051604632125747307341249759676250
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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 the Formula section. - Peter Bala, May 02 2014
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LINKS
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FORMULA
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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,
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MAPLE
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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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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