A035987 Number of partitions of n into parts not of the form 21k, 21k+9 or 21k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 9 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 54, 73, 95, 126, 162, 211, 268, 344, 433, 549, 685, 859, 1064, 1322, 1626, 2004, 2449, 2997, 3641, 4427, 5350, 6467, 7776, 9350, 11192, 13392, 15961, 19014, 22572, 26779, 31671, 37430, 44114, 51950, 61026

Offset

1,2

Comments

Case k=10,i=9 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(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+ 9-21))*(1 - x^(21*k- 9))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A319454 A023029 A358909 * A035997 A036008 A104502

Adjacent sequences: A035984 A035985 A035986 * A035988 A035989 A035990

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved