cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A210813 Number of spanning trees in C_10 X P_n.

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%I A210813 #15 Nov 13 2015 16:08:18
%S A210813 10,2620860,321437558750,34966152200584440,3696387867279360000000,
%T A210813 387686455761449000565832500,40568852698294278820875719309510,
%U A210813 4242420895960521871557351517779467760,443556393051604632125747307341249759676250
%N A210813 Number of spanning trees in C_10 X P_n.
%C A210813 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 A210813 Alois P. Heinz, <a href="/A210813/b210813.txt">Table of n, a(n) for n = 1..50</a>
%H A210813 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A210813 From _Peter Bala_, May 02 2014: (Start)
%F A210813 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 A210813 a(n) = 10*A001109(n) * A241606(n)^2 * A143699(n)^2 = 2*A001109(n) * A241606(n)^2 * A003733(n). (End)
%p A210813 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 A210813 10th column of A173958.
%Y A210813 Cf. A001109, A003733, A143699, A241606.
%K A210813 nonn,easy
%O A210813 1,1
%A A210813 _Alois P. Heinz_, Mar 26 2012