A087154 Number of partitions of n into distinct nonsquares.

1, 0, 1, 1, 0, 2, 1, 2, 3, 2, 4, 4, 4, 7, 6, 9, 9, 11, 14, 14, 19, 21, 23, 29, 31, 36, 43, 46, 56, 62, 70, 81, 91, 103, 117, 132, 148, 167, 188, 211, 237, 266, 297, 332, 371, 414, 461, 515, 571, 634, 708, 780, 870, 963, 1062, 1180, 1300, 1436, 1588, 1747, 1929, 2123

Offset: 0

Author

Reinhard Zumkeller, Aug 21 2003

Keywords

• nonn

Examples

			n=7: 2+5 = 7: a(7)=2;
n=8: 2+6 = 3+5 = 8: a(8)=3;
n=9: 2+7 = 3+6: a(9)=2.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A087153, A033461, A000041, A000037.

Cf. A225045, A280264.

Programs

Haskell

a087154 = p a000037_list where
   p _      0 = 1
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
-- Reinhard Zumkeller, Apr 25 2013

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + x^k)/(1 + x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 29 2016 *)

Formula

G.f.: Product_{m>0} (1+x^m)/(1+x^(m^2)). - Vladeta Jovovic, Jul 31 2004

a(n) ~ exp(Pi*sqrt(n/3) - 3^(1/4) * (sqrt(2)-1) * Zeta(3/2) * n^(1/4) / 2 - 3*(sqrt(2)-1)^2 * Zeta(3/2)^2 / (32*Pi)) / (2^(3/2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Dec 30 2016

Extensions

Zeroth term added by Franklin T. Adams-Watters, Jan 25 2010