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

0,2

Links

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

Formula

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

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 *)

Crossrefs

Row sums of A284249.

Cf. A126024.

Sequence in context: A067904 A018146 A293637 * A291660 A069749 A081889

Adjacent sequences: A284247 A284248 A284249 * A284251 A284252 A284253

Keyword

nonn

Author

Alois P. Heinz, Mar 23 2017

Status

approved