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A193126 Numbers of spanning trees of the Andrasfai graphs. 2
1, 5, 392, 130691, 116268789, 217138318913, 735586507699560, 4097541199291485383, 34978630555104539011865, 433956321312627533863411229, 7507648403517784836450716354400, 175224359120863022267621776711423115, 5369536232535958477000676021964993713773 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 15 23:51 EDT 2022. Contains 353687 sequences. (Running on oeis4.)