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, 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, 3696, 4149, 4658, 5224, 5849, 6547

Offset

0,6

Links

Table of n, a(n) for n=0..56.

Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.

Formula

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

Example

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.

Maple

gfun[seriestolist](series(product((1+x^k)/(1-(-1)^k*x^(2*k^2-k)), k=1..100), x=0, 100))[];

Crossrefs

Cf. A014634, A100926, A100927.

Sequence in context: A296440 A181692 A145806 * A188215 A162627 A023158

Adjacent sequences: A100986 A100987 A100988 * A100990 A100991 A100992

Keyword

nonn

Author

Noureddine Chair, Nov 29 2004

Extensions

Offset corrected by Alois P. Heinz, Mar 11 2026

Status

approved