A035965 Number of partitions of n into parts not of the form 17k, 17k+4 or 17k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 7 are greater than 1.

1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 70, 92, 118, 151, 191, 243, 303, 381, 473, 587, 723, 892, 1090, 1334, 1622, 1970, 2381, 2878, 3458, 4156, 4973, 5944, 7081, 8429, 9996, 11848, 14001, 16527, 19459, 22891, 26858, 31486, 36831, 43036, 50190

Offset

1,2

Comments

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

Crossrefs

Sequence in context: A335754 A105781 A035958 * A035973 A035982 A035992

Adjacent sequences: A035962 A035963 A035964 * A035966 A035967 A035968

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved