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A035966 Number of partitions of n into parts not of the form 17k, 17k+5 or 17k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 7 are greater than 1. 0
1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 61, 78, 103, 131, 170, 213, 273, 340, 429, 531, 663, 814, 1008, 1230, 1509, 1833, 2233, 2695, 3264, 3921, 4719, 5644, 6758, 8046, 9590, 11372, 13492, 15942, 18838, 22177, 26110, 30637, 35941, 42043, 49162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=8,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(7*n/51)) * 7^(1/4) * cos(7*Pi/34) / (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+ 5-17))*(1 - x^(17*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A341154 A035959 A036801 * A035974 A035983 A035993

Adjacent sequences:  A035963 A035964 A035965 * A035967 A035968 A035969

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.)