A193126 Numbers of spanning trees of the Andrásfai graphs.

1, 5, 392, 130691, 116268789, 217138318913, 735586507699560, 4097541199291485383, 34978630555104539011865, 433956321312627533863411229, 7507648403517784836450716354400, 175224359120863022267621776711423115, 5369536232535958477000676021964993713773

Offset

1,2

Comments

Is it obvious that, beyond the prime a(2) = 5, all values shown are not squarefree (i.e., in A013929). For example, a(10) = 29 * 59^2 * 65564989939^2. - Jonathan Vos Post, Jul 16 2011

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Andrásfai Graph

Eric Weisstein's World of Mathematics, Spanning Tree

Maple

with(LinearAlgebra):
a:= proc(n) local h, i, M, m;
      m:= 3*n-1;
      M:= Matrix(m, shape=symmetric);
      for h in [seq(seq(`if`(irem(j-i, 3)=1, [i, j], NULL),
                i=1..j-1), j=2..m)]
      do M[h[]]:= -1 od;
      for i to m do M[i, i]:= -add(M[i, j], j=1..m) od;
      Determinant(DeleteColumn(DeleteRow(M, 1), 1))
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Jul 18 2011

Mathematica

a[n_] := Module[{M, m = 3n-1}, M[_, _] = 0; Do[M[Sequence @@ h] = -1, {h, Flatten[Table[Table[If[Mod[j - i, 3] == 1, {i, j}, Nothing], {i, 1, j - 1}], {j, 2, m}], 1]}]; For[i = 1, i <= m, i++, M[i, i] = -Sum[If[j >= i, M[i, j], M[j, i]], {j, 1, m}]]; Det[Table[If[j >= i, M[i, j], M[j, i]], {i, 2, m}, {j, 2, m}]]];
Array[a, 20](* Jean-François Alcover, Nov 12 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A060506 A302394 A057633 * A006700 A079011 A195502

Adjacent sequences: A193123 A193124 A193125 * A193127 A193128 A193129

Keyword

nonn

Author

Eric W. Weisstein, Jul 16 2011

Extensions

More terms from Alois P. Heinz, Jul 18 2011

Status

approved