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A087154 Number of partitions of n into distinct nonsquares. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A250099

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

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Last modified December 12 17:13 EST 2018. Contains 318079 sequences. (Running on oeis4.)