%I #35 Feb 09 2024 03:59:01
%S 1,5,392,130691,116268789,217138318913,735586507699560,
%T 4097541199291485383,34978630555104539011865,
%U 433956321312627533863411229,7507648403517784836450716354400,175224359120863022267621776711423115,5369536232535958477000676021964993713773
%N Numbers of spanning trees of the Andrásfai graphs.
%C 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
%H Alois P. Heinz, <a href="/A193126/b193126.txt">Table of n, a(n) for n = 1..100</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AndrasfaiGraph.html">Andrásfai Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>
%p with(LinearAlgebra):
%p a:= proc(n) local h, i, M, m;
%p m:= 3*n-1;
%p M:= Matrix(m, shape=symmetric);
%p for h in [seq(seq(`if`(irem(j-i, 3)=1, [i,j], NULL),
%p i=1..j-1), j=2..m)]
%p do M[h[]]:= -1 od;
%p for i to m do M[i, i]:= -add(M[i, j], j=1..m) od;
%p Determinant(DeleteColumn(DeleteRow(M, 1), 1))
%p end:
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Jul 18 2011
%t 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}]]];
%t Array[a, 20](* _Jean-François Alcover_, Nov 12 2020, after _Alois P. Heinz_ *)
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Jul 16 2011
%E More terms from _Alois P. Heinz_, Jul 18 2011
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