A158880 Number of spanning trees in C_6 X P_n.

6, 8100, 7741440, 7138643400, 6551815840350, 6009209192448000, 5511006731579419434, 5054037303588059379600, 4634949992739663836897280, 4250612670512943969574312500, 3898145031429828405122837863554

Offset: 1

Author

Alois P. Heinz, Mar 28 2009

Keywords

• nonn
• easy

Comments

A linear divisibility sequence of order 18. - Peter Bala, May 02 2014

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Cycle Graph
• Eric Weisstein's World of Mathematics, Path Graph
• Eric Weisstein's World of Mathematics, Spanning Tree
• Index to divisibility sequences

Crossrefs

Column 6 of A173958.

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

Programs

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);

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