cp's OEIS Frontend

A087154 Number of partitions of n into distinct nonsquares.

%I A087154 #22 Jan 20 2025 12:36:54
%S A087154 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,
%T A087154 56,62,70,81,91,103,117,132,148,167,188,211,237,266,297,332,371,414,
%U A087154 461,515,571,634,708,780,870,963,1062,1180,1300,1436,1588,1747,1929,2123
%N A087154 Number of partitions of n into distinct nonsquares.
%H A087154 Vaclav Kotesovec, <a href="/A087154/b087154.txt">Table of n, a(n) for n = 0..10000</a>
%F A087154 G.f.: Product_{m>0} (1+x^m)/(1+x^(m^2)). - _Vladeta Jovovic_, Jul 31 2004
%F A087154 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
%e A087154 n=7: 2+5 = 7: a(7)=2;
%e A087154 n=8: 2+6 = 3+5 = 8: a(8)=3;
%e A087154 n=9: 2+7 = 3+6: a(9)=2.
%t A087154 nmax = 100; CoefficientList[Series[Product[(1 + x^k)/(1 + x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 29 2016 *)
%o A087154 (Haskell)
%o A087154 a087154 = p a000037_list where
%o A087154    p _      0 = 1
%o A087154    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
%o A087154 -- _Reinhard Zumkeller_, Apr 25 2013
%Y A087154 Cf. A087153, A033461, A000041, A000037.
%Y A087154 Cf. A225045, A280264.
%K A087154 nonn
%O A087154 0,6
%A A087154 _Reinhard Zumkeller_, Aug 21 2003
%E A087154 Zeroth term added by _Franklin T. Adams-Watters_, Jan 25 2010