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A035983 Number of partitions of n into parts not of the form 21k, 21k+5 or 21k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 9 are greater than 1. 0
1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 105, 134, 174, 219, 282, 352, 446, 554, 694, 855, 1063, 1301, 1602, 1952, 2386, 2889, 3511, 4231, 5109, 6130, 7363, 8794, 10515, 12507, 14885, 17642, 20910, 24690, 29157, 34313, 40373, 47366, 55547 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=10,i=5 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)) * sin(5*Pi/21) / (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+ 5-21))*(1 - x^(21*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A036801 A035966 A035974 * A035993 A036004 A027339

Adjacent sequences:  A035980 A035981 A035982 * A035984 A035985 A035986

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)