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A035986 Number of partitions of n into parts not of the form 21k, 21k+8 or 21k-8. Also number of partitions with at most 7 parts of size 1 and differences between parts at distance 9 are greater than 1. 0
1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72, 93, 123, 159, 206, 262, 336, 423, 535, 669, 837, 1037, 1288, 1584, 1950, 2385, 2915, 3542, 4305, 5202, 6284, 7558, 9082, 10871, 13004, 15498, 18454, 21909, 25982, 30727, 36306, 42785, 50371, 59170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=10,i=8 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..45.

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/7)) * cos(5*Pi/42) / (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+ 8-21))*(1 - x^(21*k- 8))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A288256 A101049 A333193 * A035996 A261775 A036007

Adjacent sequences:  A035983 A035984 A035985 * A035987 A035988 A035989

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.)