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

1,6

Comments

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

Links

Table of n, a(n) for n=1..58.

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.

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))

Example

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"

Maple

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

Crossrefs

Sequence in context: A328399 A328171 A029139 * A001687 A159072 A116928

Adjacent sequences: A100924 A100925 A100926 * A100928 A100929 A100930

Keyword

nonn

Author

Noureddine Chair, Nov 22 2004

Status

approved