OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..50
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Spanning Tree
FORMULA
a(n) = 3*8^(n-1)*n^(3*n-2).
MAPLE
with(LinearAlgebra):
a:= proc(n) local h, i, M;
M:= Matrix(3*n, shape=symmetric);
for h in [seq(seq([[i, j+n], [i, j+2*n], [i+n, j+2*n]][],
j=1..n), i=1..n)]
do M[h[]]:= -1 od;
for i to 3*n do M[i, i]:= -add(M[i, j], j=1..3*n) od;
Determinant(DeleteColumn(DeleteRow(M, 1), 1))
end:
seq(a(n), n=1..12); # Alois P. Heinz, Jul 18 2011
MATHEMATICA
Table[3 8^(n - 1) n^(3 n - 2), {n, 11}]
PROG
(PARI) a(n)=3*n^(3*n-2)<<(3*n-3) \\ Charles R Greathouse IV, Jul 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 16 2011
EXTENSIONS
More terms from Alois P. Heinz, Jul 18 2011
STATUS
approved