A100927 Number of partitions of n into distinct parts free of hexagonal numbers.

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, 66, 76, 87, 100, 113, 129, 147, 167, 189, 214, 241, 273, 307, 345, 388, 436, 489, 548, 612, 686, 765, 854, 951, 1059, 1180, 1309, 1456, 1614, 1791, 1985, 2196

Offset: 1

Author

Noureddine Chair, Nov 22 2004

Keywords

• nonn

Comments

This is also the inverted graded of the generating function of partitions into parts free of hexagonal numbers

Examples

			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"
		

Links

• Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.
• James A. Sellers, Partitions Excluding Specific Polygonal Numbers As Parts, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.

Programs

Maple

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

Formula

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))