A026906 Number of sums S of distinct positive integers satisfying S <= n.

1, 2, 4, 6, 9, 13, 18, 24, 32, 42, 54, 69, 87, 109, 136, 168, 206, 252, 306, 370, 446, 535, 639, 761, 903, 1068, 1260, 1482, 1738, 2034, 2374, 2764, 3212, 3724, 4309, 4977, 5737, 6601, 7583, 8696, 9956, 11382, 12992, 14808, 16856

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			G.f. = x + 2*x^2 + 4*x^3 + 6*x^4 + 9*x^5 + 13*x^6 + 18*x^7 + 24*x^8 + 32*x^9 + ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Partial sums of A000009.

Cf. A000070.

Programs

Mathematica

Table[ Sum[ PartitionsQ[k], {k, 1, n}], {n, 1, 50}]

Formula

a(n) ~ exp(Pi*sqrt(n/3)) * 3^(1/4) / (2*Pi*n^(1/4)) * (1 + (18+13*Pi^2) / (48*Pi*sqrt(3*n))). - Vaclav Kotesovec, Oct 25 2016

a(n) = A036469(n) - 1. - Vaclav Kotesovec, Oct 26 2016

G.f.: -1/(1 - x) + (1/(1 - x))*Product_{k>=1} (1 + x^k). - Ilya Gutkovskiy, Dec 25 2016