A100989 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.
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, 112, 131, 154, 178, 207, 242, 277, 321, 371, 425, 489, 562, 641, 733, 839, 953, 1086, 1236, 1399, 1588, 1798, 2032, 2295, 2592, 2917, 3285
Offset: 1
Keywords
Examples
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"
Links
- Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.
Programs
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Maple
series(product((1+x^k)/(1-(-1)^k*x^(2*k^2-k)),k=1..100),x=0,100);
Formula
G.f.: product_{k>0}(1+x^k)/(1-(-1)^k*x^(2*k^2-k)).