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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 16 2011
EXTENSIONS
More terms from Alois P. Heinz, Jul 18 2011
STATUS
approved