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

0,6

Links

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

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A087153, A033461, A000041, A000037.

Cf. A225045, A280264.

Sequence in context: A290370 A029166 A096920 * A029839 A082304 A321664

Adjacent sequences: A087151 A087152 A087153 * A087155 A087156 A087157

Keyword

nonn

Author

Reinhard Zumkeller, Aug 21 2003

Extensions

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

Status

approved