A035981 Number of partitions in parts not of the form 21k, 21k+3 or 21k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 9 are greater than 1.

1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 208, 258, 328, 404, 507, 621, 772, 941, 1159, 1406, 1719, 2075, 2520, 3028, 3656, 4374, 5252, 6259, 7479, 8879, 10561, 12493, 14800, 17448, 20590, 24196, 28453, 33335, 39069, 45641

Offset

1,2

Comments

Case k=10,i=3 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..47.

Formula

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

Crossrefs

Sequence in context: A035957 A035964 A035972 * A035991 A036002 A104504

Adjacent sequences: A035978 A035979 A035980 * A035982 A035983 A035984

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved