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A035941 Number of partitions of n into parts not of the form 9k, 9k+2 or 9k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 3 are greater than 1. 1
1, 1, 2, 3, 4, 6, 7, 10, 13, 17, 21, 28, 35, 44, 55, 69, 84, 105, 127, 156, 189, 229, 275, 333, 397, 475, 565, 673, 795, 943, 1109, 1307, 1533, 1798, 2099, 2455, 2855, 3323, 3855, 4472, 5169, 5978, 6890, 7942, 9132, 10495, 12032, 13796, 15778, 18040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Case k=4, i=2 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..50.

FORMULA

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

MAPLE

# See A035937 for GordonsTheorem

A035941_list := n -> GordonsTheorem([1, 0, 1, 1, 1, 1, 0, 1, 0], n):

A035941_list(40); # Peter Luschny, Jan 22 2012

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-3)) * (1 - x^(9*k-4)) * (1 - x^(9*k-5)) * (1 - x^(9*k-6)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 12 2015 *)

PROG

(Sage) # See A035937 for GordonsTheorem

def A035941_list(len) :  return GordonsTheorem([1, 0, 1, 1, 1, 1, 0, 1, 0], len)

A035941_list(40) # Peter Luschny, Jan 22 2012

CROSSREFS

Sequence in context: A119793 A181436 A199118 * A039854 A237752 A032480

Adjacent sequences:  A035938 A035939 A035940 * A035942 A035943 A035944

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)