A035984 Number of partitions of n into parts not of the form 21k, 21k+6 or 21k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 9 are greater than 1.

1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 145, 188, 239, 305, 384, 485, 605, 756, 936, 1160, 1426, 1753, 2141, 2615, 3175, 3853, 4653, 5616, 6749, 8103, 9693, 11584, 13798, 16418, 19478, 23085, 27286, 32217, 37948, 44651, 52422, 61479

Offset

1,2

Comments

Case k=10,i=6 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..46.

Formula

a(n) ~ exp(2*Pi*sqrt(n/7)) * cos(3*Pi/14) / (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+ 6-21))*(1 - x^(21*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A097797 A219601 A035975 * A035994 A036005 A104503

Adjacent sequences: A035981 A035982 A035983 * A035985 A035986 A035987

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved