A035992 Number of partitions of n into parts not of the form 23k, 23k+4 or 23k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 10 are greater than 1.

1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 120, 154, 196, 250, 313, 395, 493, 614, 760, 941, 1155, 1419, 1733, 2113, 2565, 3112, 3756, 4531, 5445, 6533, 7815, 9338, 11120, 13230, 15697, 18599, 21986, 25960, 30578, 35980, 42250, 49550, 58006

Offset

1,2

Comments

Case k=11,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(10*n/69)) * 10^(1/4) * sin(4*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+ 4-23))*(1 - x^(23*k- 4))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035965 A035973 A035982 * A036003 A027338 A064174

Adjacent sequences: A035989 A035990 A035991 * A035993 A035994 A035995

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved