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A100927 Number of partitions of n into distinct parts free of hexagonal numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 14:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)