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Number of spanning trees in C_10 X P_n.
2

%I #15 Nov 13 2015 16:08:18

%S 10,2620860,321437558750,34966152200584440,3696387867279360000000,

%T 387686455761449000565832500,40568852698294278820875719309510,

%U 4242420895960521871557351517779467760,443556393051604632125747307341249759676250

%N Number of spanning trees in C_10 X P_n.

%C 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

%H Alois P. Heinz, <a href="/A210813/b210813.txt">Table of n, a(n) for n = 1..50</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%F From _Peter Bala_, May 02 2014: (Start)

%F 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,

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

%p 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

%Y 10th column of A173958.

%Y Cf. A001109, A003733, A143699, A241606.

%K nonn,easy

%O 1,1

%A _Alois P. Heinz_, Mar 26 2012