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A035987 Number of partitions of n into parts not of the form 21k, 21k+9 or 21k-9. Also number of partitions with at most 8 parts of size 1 and differences between parts at distance 9 are greater than 1. 0
1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 54, 73, 95, 126, 162, 211, 268, 344, 433, 549, 685, 859, 1064, 1322, 1626, 2004, 2449, 2997, 3641, 4427, 5350, 6467, 7776, 9350, 11192, 13392, 15961, 19014, 22572, 26779, 31671, 37430, 44114, 51950, 61026 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=10,i=9 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(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+ 9-21))*(1 - x^(21*k- 9))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A319475 A319454 A023029 * A035997 A036008 A104502

Adjacent sequences:  A035984 A035985 A035986 * A035988 A035989 A035990

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.)