cp's OEIS Frontend

A100926 Number of partitions of n into parts free of odd squares and the only number with multiplicity in the unrestricted partitions is the number 2.

%I A100926 #16 Dec 14 2018 07:51:10
%S A100926 1,0,1,1,2,2,3,4,5,6,8,10,12,15,18,23,27,33,40,48,57,69,81,97,113,134,
%T A100926 157,184,214,250,290,337,389,451,519,598,688,789,904,1035,1181,1348,
%U A100926 1535,1746,1983,2250,2549,2885,3261,3682,4154,4680,5268,5923,6656,7468
%N A100926 Number of partitions of n into parts free of odd squares and the only number with multiplicity in the unrestricted partitions is the number 2.
%C A100926 This is also the inverted graded generating function for the number of partitions in which no square parts are present
%H A100926 Noureddine Chair, <a href="http://arxiv.org/abs/hep-th/0409011">Partition Identities From Partial Supersymmetry</a>, arXiv:hep-th/0409011v1, 2004.
%H A100926 James A. Sellers, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Sellers/sellers58.html">Partitions Excluding Specific Polygonal Numbers As Parts</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.
%F A100926 G.f.: Product_{k>=0}(1+x^k)/(1-(-1)^k*x^(k^2)).
%e A100926 a(10)=8 because 10 =8+2 =7+3 =6+4 =5+3+2 =6+2+2 =4+2+2+2 =2+2+2+2+2.
%p A100926 series(product((1+x^k)/(1-(-1)^k*x^(k^2)),k=1..100),x=0,100);
%t A100926 terms = 56; Product[(1 + x^k)/(1 - (-1)^k*x^(k^2)), {k, 1, terms}] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Dec 14 2018 *)
%K A100926 nonn
%O A100926 1,5
%A A100926 _Noureddine Chair_, Nov 22 2004