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.

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

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