A035986 Number of partitions of n into parts not of the form 21k, 21k+8 or 21k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 9 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72, 93, 123, 159, 206, 262, 336, 423, 535, 669, 837, 1037, 1288, 1584, 1950, 2385, 2915, 3542, 4305, 5202, 6284, 7558, 9082, 10871, 13004, 15498, 18454, 21909, 25982, 30727, 36306, 42785, 50371, 59170

Offset

1,2

Comments

Case k=10,i=8 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Table of n, a(n) for n=1..45.

Formula

a(n) ~ exp(2*Pi*sqrt(n/7)) * cos(5*Pi/42) / (sqrt(3) * 7^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 8-21))*(1 - x^(21*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A288256 A101049 A333193 * A035996 A261775 A036007

Adjacent sequences: A035983 A035984 A035985 * A035987 A035988 A035989

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved