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A161091 Number of partitions of n into squares where every part appears at least 3 times.

%I A161091 #15 Jun 15 2025 08:28:50
%S A161091 0,0,1,1,1,1,1,1,1,1,1,2,1,1,2,3,2,2,3,4,3,3,4,5,4,4,6,6,5,6,7,8,7,7,
%T A161091 8,10,8,8,11,11,10,11,13,13,13,13,15,18,15,16,20,21,19,21,23,24,24,24,
%U A161091 27,30,28,28,33,36,33,35,39,42,41,42,45,49,47,48,55,56,54,58,63,67,65,66,72,78
%N A161091 Number of partitions of n into squares where every part appears at least 3 times.
%H A161091 R. H. Hardin, <a href="/A161091/b161091.txt">Table of n, a(n) for n = 1..1000</a>
%F A161091 G.f.: Product_{j>=1} (1 + x^(3j^2)/(1-x^(j^2))). - _Emeric Deutsch_, Jun 24 2009
%e A161091 a(23)=4 because we have (4^5)(1^3), (4^4)(1^7), (4^3)(1^11), and (1^23). - _Emeric Deutsch_, Jun 24 2009
%p A161091 g := product(1+x^(3*j^2)/(1-x^(j^2)), j = 1 .. 20): gser := series(g, x = 0, 90): seq(coeff(gser, x, n), n = 2 .. 84); # _Emeric Deutsch_, Jun 24 2009
%t A161091 nmax = 100; Rest[CoefficientList[Series[Product[(1 + x^(3*k^2)/(1-x^(k^2))), {k, 1, Sqrt[nmax]+1}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jun 15 2025 *)
%Y A161091 Cf. A001156, A103265.
%K A161091 nonn
%O A161091 1,12
%A A161091 _R. H. Hardin_, Jun 02 2009