A100928 Number of partitions of n into parts free of odd octagonal (star) numbers: k(3k-2) and the only number with multiplicity in the unrestricted partitions is the number 2 with multiplicity of the form :4k+2l, k a positive integer and l=0,1.

1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 18, 21, 26, 31, 37, 44, 52, 62, 73, 86, 101, 118, 138, 160, 186, 216, 249, 288, 332, 381, 438, 501, 573, 655, 746, 851, 966, 1099, 1244, 1410, 1595, 1801, 2033, 2292, 2580, 2903, 3261, 3660, 4105, 4598, 5147, 5755

Offset

1,6

Comments

This is also the inverted graded of the generating function for partitions of n into parts free of octagonal numbers.

Links

Table of n, a(n) for n=1..57.

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-(-1)^k*x^(3*k^2-2k)).

Example

a(15)=18 because 15 =13+5 =12+3 =11+4 =10+5 =10+3+2 =9+6 =9+4+2 =8+7 =8+4+3 =8+5+2 =7+6+2 =7+5+3 =6+5+4 =6+4+3+2 =5+2+2+2+2+2 =7+2+2+2+2 =4+3+2+2+2+2.

Maple

series(product((1+x^k)/(1-(-1)^k*x^(3*k^(2)-2*k)), k=1..100), x=0, 100);

Crossrefs

Sequence in context: A185225 A027196 A325877 * A240671 A034140 A109950

Adjacent sequences: A100925 A100926 A100927 * A100929 A100930 A100931

Keyword

nonn

Author

Noureddine Chair, Nov 23 2004

Status

approved