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A158880 Number of spanning trees in C_6 X P_n. 5

%I #17 Nov 13 2015 15:38:04

%S 6,8100,7741440,7138643400,6551815840350,6009209192448000,

%T 5511006731579419434,5054037303588059379600,4634949992739663836897280,

%U 4250612670512943969574312500,3898145031429828405122837863554

%N Number of spanning trees in C_6 X P_n.

%C A linear divisibility sequence of order 18. - _Peter Bala_, May 02 2014

%H Alois P. Heinz, <a href="/A158880/b158880.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PathGraph.html">Path Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>

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

%F See program.

%F a(n) = 6*U(n-1,3/2)^2*U(n-1,5/2)^2*U(n-1,3) = 6*A001906(n)^2*A004254(n)^2*A001109(n), where U(n,x) is a Chebyshev polynomial of the second kind. - _Peter Bala_, May 02 2014

%p a:= n-> 6* (Matrix(1,18, (i,j)-> -sign(j-10) *[0, 1, 1350, 1290240, 1189773900, 1091969306725, 1001534865408000, 918501121929903239, 842339550598009896600, 772491665456610639482880][1+abs(j-10)]). Matrix(18, (i,j)-> if i=j-1 then 1 elif j=1 then [842608511100, -639641521152, 276457068288, -65829977967, 8292106368, -524839680, 16393554, -232704, 1152, -1][1+abs(i-9)] else 0 fi)^n) [1,10]: seq(a(n), n=1..15);

%Y Column 6 of A173958.

%Y Cf. A001353, A003690, A003753, A003733, A158898. A001109, A001906, A004254.

%K nonn,easy

%O 1,1

%A _Alois P. Heinz_, Mar 28 2009

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)