A035991 Number of partitions in parts not of the form 23k, 23k+3 or 23k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 10 are greater than 1.

1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 209, 259, 329, 406, 510, 625, 778, 949, 1170, 1420, 1738, 2100, 2553, 3070, 3710, 4443, 5340, 6369, 7618, 9052, 10777, 12760, 15130, 17853, 21088, 24803, 29193, 34233, 40158, 46954

Offset

1,2

Comments

Case k=11,i=3 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(10*n/69)) * 10^(1/4) * sin(3*Pi/23) / (3^(1/4) * 23^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 3-23))*(1 - x^(23*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035964 A035972 A035981 * A036002 A104504 A027337

Adjacent sequences: A035988 A035989 A035990 * A035992 A035993 A035994

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved