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

1,5

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A058377, A112972.

Sequence in context: A077628 A213280 A056862 * A374195 A099447 A078067

Adjacent sequences: A113032 A113033 A113034 * A113036 A113037 A113038

Keyword

nonn

Author

Floor van Lamoen, Oct 11 2005

Status

approved