A113035 Number of ways the set {1,2,...,n} can be split into two subsets of which the sum of one is twice the sum of the other.

0, 1, 1, 0, 3, 4, 0, 10, 17, 0, 46, 78, 0, 231, 401, 0, 1233, 2177, 0, 6869, 12268, 0, 39502, 71172, 0, 232686, 422076, 0, 1396669, 2547246, 0, 8512170, 15593760, 0, 52534875, 96598865, 0, 327669853, 604405633, 0, 2062171364, 3814087419, 0, 13078921499

Offset: 1

Author

Floor van Lamoen, Oct 11 2005

Keywords

• nonn

Examples

			For n=5 we have 5/1234, 14/532 and 23/541 so a(5)=3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A058377, A112972.

Programs

Maple

A113035:= proc(n) local i,j,p,t; t:= NULL; for j to n do p:=1; for i to j do p:=p*(x^(-2*i)+x^(i)); od; t:=t,coeff(p,x,0); od; t; end;
# second Maple program:
b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;
      `if`(n>m, 0, `if`(n=m, 1, b(abs(n-i), i-1) +b(n+i, i-1)))
    end:
a:= n-> `if`(irem(n, 3)=1, 0, b(n*(n+1)/6, n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Oct 31 2011

Mathematica

b[n_, i_] := b[n, i] = Module[{m = i(i+1)/2}, If[n > m, 0, If[n == m, 1, b[Abs[n - i], i - 1] + b[n + i, i - 1]]]];
a[n_] := If[Mod[n, 3] == 1, 0, b[n(n+1)/6, n]];
Array[a, 60] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)

Formula

a(n) is the coefficient of x^0 in Product_{k=1..n} x^(-2k)+x^k.