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A035984 Number of partitions of n into parts not of the form 21k, 21k+6 or 21k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 9 are greater than 1. 0
1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 145, 188, 239, 305, 384, 485, 605, 756, 936, 1160, 1426, 1753, 2141, 2615, 3175, 3853, 4653, 5616, 6749, 8103, 9693, 11584, 13798, 16418, 19478, 23085, 27286, 32217, 37948, 44651, 52422, 61479 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=10,i=6 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..46.

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/7)) * cos(3*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+ 6-21))*(1 - x^(21*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A097797 A219601 A035975 * A035994 A036005 A104503

Adjacent sequences:  A035981 A035982 A035983 * A035985 A035986 A035987

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 12 09:05 EDT 2020. Contains 336438 sequences. (Running on oeis4.)