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.

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

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