A284250 - OEIS

%I #13 Mar 17 2022 11:42:02

%S 1,2,3,5,7,11,18,29,49,85,151,271,493,904,1674,3118,5835,10966,20698,

%T 39187,74413,141684,270386,517110,990889,1902108,3657241,7042490,

%U 13580079,26220417,50687371,98095126,190042856,368539253,715349145,1389731960,2702098563

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

%H Alois P. Heinz, <a href="/A284250/b284250.txt">Table of n, a(n) for n = 0..600</a>

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

%p b:= proc(n, s) option remember; `if`(n=0,

%p       `if`(issqr(8*s+1), 1, 0), b(n-1, s)+b(n-1, s+n))

%p     end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=0..40);

%t b[n_, s_] := b[n, s] = If[n == 0,

%t      If[IntegerQ@Sqrt[8*s + 1], 1, 0], b[n - 1, s] + b[n - 1, s + n]];

%t a[n_] := b[n, 0];

%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Mar 17 2022, after _Alois P. Heinz_ *)

%Y Row sums of A284249.

%Y Cf. A126024.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Mar 23 2017