A193131 Numbers of spanning trees of the complete tripartite graphs K_{n,n,n}.

3, 384, 419904, 1610612736, 15000000000000, 277326388342554624, 8964455938423371595776, 464227514732017603087171584, 36132988816414656965872925540352, 4026531840000000000000000000000000000, 618293049656826371620197206797522978209792

Offset: 1

Author

Eric W. Weisstein, Jul 16 2011

Keywords

• nonn
• easy

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

Programs

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}]

PARI

a(n)=3*n^(3*n-2)<<(3*n-3) \\ Charles R Greathouse IV, Jul 29 2011

Formula

a(n) = 3*8^(n-1)*n^(3*n-2).

Extensions

More terms from Alois P. Heinz, Jul 18 2011