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

%I A284250 #13 Mar 17 2022 11:42:02
%S A284250 1,2,3,5,7,11,18,29,49,85,151,271,493,904,1674,3118,5835,10966,20698,
%T A284250 39187,74413,141684,270386,517110,990889,1902108,3657241,7042490,
%U A284250 13580079,26220417,50687371,98095126,190042856,368539253,715349145,1389731960,2702098563
%N A284250 Number of subsets of [n] whose sum is a triangular number.
%H A284250 Alois P. Heinz, <a href="/A284250/b284250.txt">Table of n, a(n) for n = 0..600</a>
%F A284250 a(n) = Sum_{k=0..n} A284249(n,k).
%p A284250 b:= proc(n, s) option remember; `if`(n=0,
%p A284250       `if`(issqr(8*s+1), 1, 0), b(n-1, s)+b(n-1, s+n))
%p A284250     end:
%p A284250 a:= n-> b(n, 0):
%p A284250 seq(a(n), n=0..40);
%t A284250 b[n_, s_] := b[n, s] = If[n == 0,
%t A284250      If[IntegerQ@Sqrt[8*s + 1], 1, 0], b[n - 1, s] + b[n - 1, s + n]];
%t A284250 a[n_] := b[n, 0];
%t A284250 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Mar 17 2022, after _Alois P. Heinz_ *)
%Y A284250 Row sums of A284249.
%Y A284250 Cf. A126024.
%K A284250 nonn
%O A284250 0,2
%A A284250 _Alois P. Heinz_, Mar 23 2017