%I #9 Apr 27 2013 09:52:40

%S 1,0,1,1,1,2,3,3,4,6,6,9,11,13,16,20,20,23,29,35,41,49,59,68,82,96,

%T 112,131,154,178,207,242,277,321,371,425,489,562,641,733,839,953,1086,

%U 1236,1399,1588,1798,2032,2295,2592,2917,3285

%N Number of partitions of n into parts free of odd hexagonal numbers and the only number with multiplicity in the unrestricted partitions is the number 2 with multiplicity of the form 3k+l, where k is a positive integer and l=0,1.

%H Noureddine Chair, <a href="http://arxiv.org/abs/hep-th/0409011">Partition Identities From Partial Supersymmetry</a>, arXiv:hep-th/0409011v1, 2004.

%F G.f.: product_{k>0}(1+x^k)/(1-(-1)^k*x^(2*k^2-k)).

%e a(15)=20 because 15 =13+2 =12+3 =11+4 =10+5 =10+3+2 =9+6=9+4+2 =8+7 =8+5+2 =8+4+3 =7+6+2 =7+5+3 =6+5+4 =6+4+3+2 =9+2+2+2 =7+2+2+2+2 =6+3+2+2+2 =5+4+2+2+2 =4+3+2+2+2+2 =3+2+2+2+2+2+2"

%p series(product((1+x^k)/(1-(-1)^k*x^(2*k^2-k)),k=1..100),x=0,100);

%Y Cf. A100926, A100927.

%K nonn

%O 1,6

%A _Noureddine Chair_, Nov 29 2004