A284250 Number of subsets of [n] whose sum is a triangular number.

1, 2, 3, 5, 7, 11, 18, 29, 49, 85, 151, 271, 493, 904, 1674, 3118, 5835, 10966, 20698, 39187, 74413, 141684, 270386, 517110, 990889, 1902108, 3657241, 7042490, 13580079, 26220417, 50687371, 98095126, 190042856, 368539253, 715349145, 1389731960, 2702098563

Offset: 0

Author

Alois P. Heinz, Mar 23 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..600

Crossrefs

Row sums of A284249.

Cf. A126024.

Programs

Maple

b:= proc(n, s) option remember; `if`(n=0,
      `if`(issqr(8*s+1), 1, 0), b(n-1, s)+b(n-1, s+n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..40);

Mathematica

b[n_, s_] := b[n, s] = If[n == 0,
     If[IntegerQ@Sqrt[8*s + 1], 1, 0], b[n - 1, s] + b[n - 1, s + n]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 17 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..n} A284249(n,k).