A193153 Numbers of spanning trees in the graph join of C_n and C_n.

1296, 82944, 9150625, 1575296100, 391476713761, 132821015040000, 59042071787233536, 33317165538875522500, 23276866101199344597601, 19729668557004748392960000, 19950922411933407541569256321, 23731310247317631978185581240644

Offset

3,1

Comments

The graph join is the graph obtained by adding all possible edges between different graphs to the graph union.

Links

Alois P. Heinz, Table of n, a(n) for n = 3..80

Eric Weisstein's World of Mathematics, Spanning Tree

Maple

with(LinearAlgebra):
a:= proc(n) local h, i, M;
      M:= Matrix(2*n, shape=symmetric);
      for h in [seq(seq([i, j+n], j=1..n), i=1..n),
                seq([[i, 1+(i mod n)], [n+i, n+1+(i mod n)]][], i=1..n)]
      do M[h[]]:= -1 od;
      for i to 2*n do M[i, i]:= -add(M[i, j], j=1..2*n) od;
      Determinant(DeleteColumn(DeleteRow(M, 1), 1))
    end:
seq(a(n), n=3..20);  # Alois P. Heinz, Jul 17 2011

Mathematica

a[n_] := Module[{h, i, M}, M = Array[0&, {2n, 2n}]; Do[M[[Sequence@@h]] = M[[Sequence@@Reverse[h]]] = -1, {h, Flatten[Table[{i, j+n}, {i, 1, n}, {j, 1, n}], 1] ~Join~ Flatten[Table[{{i, 1+Mod[i, n]}, {n+i, n+1 + Mod[i, n]}}, {i, 1, n}], 1]}]; For[i = 1, i <= 2n, i++, M[[i, i]] = -Sum[M[[i, j]], {j, 1, 2n}]]; Det[Rest /@ Rest[M]]];
Table[a[n], {n, 3, 20}] (* Jean-François Alcover, Feb 12 2023, after Alois P. Heinz *)

Crossrefs

Sequence in context: A265478 A017344 A223689 * A223273 A017464 A017596

Adjacent sequences: A193150 A193151 A193152 * A193154 A193155 A193156

Keyword

nonn

Author

Eric W. Weisstein, Jul 16 2011

Extensions

Description corrected by Eric W. Weisstein, May 10 2017

Status

approved