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A158880
Number of spanning trees in C_6 X P_n.
5
6, 8100, 7741440, 7138643400, 6551815840350, 6009209192448000, 5511006731579419434, 5054037303588059379600, 4634949992739663836897280, 4250612670512943969574312500, 3898145031429828405122837863554
OFFSET
1,1
COMMENTS
A linear divisibility sequence of order 18. - Peter Bala, May 02 2014
LINKS
Eric Weisstein's World of Mathematics, Cycle Graph
Eric Weisstein's World of Mathematics, Path Graph
Eric Weisstein's World of Mathematics, Spanning Tree
FORMULA
See program.
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
MAPLE
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);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 28 2009
STATUS
approved