A035940 Number of partitions in parts not of the form 9k, 9k+1 or 9k-1. Also number of partitions with no part of size 1 and differences between parts at distance 3 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 12, 17, 19, 26, 31, 40, 47, 61, 71, 90, 106, 131, 154, 190, 222, 270, 317, 381, 445, 533, 620, 737, 857, 1011, 1173, 1379, 1593, 1863, 2151, 2503, 2881, 3343, 3837, 4435, 5083, 5853, 6693, 7688, 8769, 10043, 11437, 13061

Offset

1,4

Comments

Case k=4, i=1 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..52.

Formula

a(n) ~ exp(2*Pi*sqrt(n)/3) / (6 * (1+2*cos(2*Pi/9)) * n^(3/4)). - Vaclav Kotesovec, Nov 12 2015

Maple

# See A035937 for GordonsTheorem
A035940_list := n -> GordonsTheorem([0, 1, 1, 1, 1, 1, 1, 0, 0], n):
A035940_list(40) # Peter Luschny, Jan 22 2012

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(9*k-2)) * (1 - x^(9*k-3)) * (1 - x^(9*k-4)) * (1 - x^(9*k-5)) * (1 - x^(9*k-6)) * (1 - x^(9*k-7)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 12 2015 *)

Prog

(Sage) # See A035937 for GordonsTheorem
def A035940_list(len) :  return GordonsTheorem([0, 1, 1, 1, 1, 1, 1, 0, 0], len)
A035940_list(40) # Peter Luschny, Jan 22 2012

Crossrefs

Sequence in context: A001996 A317084 A122134 * A067772 A078374 A366129

Adjacent sequences: A035937 A035938 A035939 * A035941 A035942 A035943

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved