A035982 Number of partitions of n into parts not of the form 21k, 21k+4 or 21k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 9 are greater than 1.

1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 195, 249, 312, 393, 490, 610, 754, 933, 1144, 1404, 1713, 2087, 2531, 3068, 3699, 4458, 5352, 6416, 7667, 9153, 10889, 12943, 15342, 18162, 21448, 25302, 29775, 35003, 41064, 48116, 56274

Offset

1,2

Comments

Case k=10,i=4 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(4*Pi/21) / (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+ 4-21))*(1 - x^(21*k- 4))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035958 A035965 A035973 * A035992 A036003 A027338

Adjacent sequences: A035979 A035980 A035981 * A035983 A035984 A035985

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved