A035994 Number of partitions of n into parts not of the form 23k, 23k+6 or 23k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 10 are greater than 1.

1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 146, 189, 240, 307, 387, 489, 611, 764, 947, 1175, 1446, 1779, 2176, 2660, 3233, 3928, 4749, 5737, 6902, 8295, 9934, 11884, 14170, 16877, 20045, 23780, 28136, 33254, 39210, 46180, 54273, 63711

Offset

1,2

Comments

Case k=11,i=6 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(10*n/69)) * 10^(1/4) * cos(11*Pi/46) / (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+ 6-23))*(1 - x^(23*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A219601 A035975 A035984 * A036005 A104503 A027340

Adjacent sequences: A035991 A035992 A035993 * A035995 A035996 A035997

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved