OFFSET
1,1
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
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