%I #12 Jan 27 2019 09:54:12
%S 1,0,1,1,1,2,1,3,2,4,4,5,7,7,10,10,13,15,17,21,23,29,32,38,44,50,59,
%T 66,76,87,100,113,129,147,167,189,214,241,273,307,345,388,436,489,548,
%U 612,686,765,854,951,1059,1180,1309,1456,1614,1791,1985,2196
%N Number of partitions of n into distinct parts free of hexagonal numbers.
%C This is also the inverted graded of the generating function of partitions into parts free of hexagonal numbers
%H Noureddine Chair, <a href="http://arxiv.org/abs/hep-th/0409011">Partition Identities From Partial Supersymmetry</a>, arXiv:hep-th/0409011v1, 2004.
%H 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 G.f.:=product_{k>0}(1+x^k)/(1+x^(2k^2-k))= 1/product_{k>0}(1-x^k+x^(2k)-x^(3k)+...-x^(2k^2-3k)+x^(2k^2-2k))
%e E.g"a(16)=13 because 16=14+2=13+3=12+4=11+5=11+3+2=10+4+2=9+7=9+5+2=9+4+3=8+5+3=7+5+4=7+4+3+2"
%p series(product((1+x^k)/(1+x^(2*k^(2)-k)),k=1..100),x=0,100);
%K nonn
%O 1,6
%A _Noureddine Chair_, Nov 22 2004