A087154 - OEIS

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

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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