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A035982 Number of partitions of n into parts not of the form 21k, 21k+4 or 21k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 9 are greater than 1. 0
1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 195, 249, 312, 393, 490, 610, 754, 933, 1144, 1404, 1713, 2087, 2531, 3068, 3699, 4458, 5352, 6416, 7667, 9153, 10889, 12943, 15342, 18162, 21448, 25302, 29775, 35003, 41064, 48116, 56274 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=10,i=4 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..47.

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/7)) * sin(4*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+ 4-21))*(1 - x^(21*k- 4))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035958 A035965 A035973 * A035992 A036003 A027338

Adjacent sequences:  A035979 A035980 A035981 * A035983 A035984 A035985

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 4 09:42 EDT 2020. Contains 334825 sequences. (Running on oeis4.)