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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. 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 (list; graph; refs; listen; history; text; internal format)
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 A242984

Adjacent sequences:  A035937 A035938 A035939 * A035941 A035942 A035943

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 23 12:38 EST 2020. Contains 332159 sequences. (Running on oeis4.)