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A035956 Number of partitions of n into parts not of the form 15k, 15k+2 or 15k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 6 are greater than 1. 0
1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 44, 57, 73, 93, 116, 147, 183, 228, 282, 348, 426, 524, 637, 775, 939, 1136, 1366, 1645, 1969, 2356, 2809, 3345, 3969, 4709, 5564, 6570, 7739, 9105, 10683, 12527, 14651, 17120, 19965, 23257, 27039, 31412, 36420 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Case k=7,i=2 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..49.

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/15)) * 2^(1/4) * sin(2*Pi/15) / (15^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 2-15))*(1 - x^(15*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A115671 A208856 A105782 * A035963 A035971 A035980

Adjacent sequences:  A035953 A035954 A035955 * A035957 A035958 A035959

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.)