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A035962 Number of partitions in parts not of the form 17k, 17k+1 or 17k-1. Also number of partitions with no part of size 1 and differences between parts at distance 7 are greater than 1. 0
0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 54, 65, 86, 103, 133, 160, 202, 243, 305, 364, 451, 540, 661, 788, 960, 1139, 1377, 1632, 1958, 2314, 2764, 3253, 3866, 4542, 5370, 6289, 7410, 8652, 10154, 11830, 13830, 16072, 18735, 21714, 25234, 29185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Case k=8,i=1 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..51.

FORMULA

a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * sin(Pi/17) / (3^(1/4) * 17^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 1-17))*(1 - x^(17*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A266781 A035955 A240015 * A240016 A035970 A240017

Adjacent sequences:  A035959 A035960 A035961 * A035963 A035964 A035965

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)