A193126 - OEIS

%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