A036004 Number of partitions of n into parts not of the form 25k, 25k+5 or 25k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 105, 134, 175, 220, 284, 355, 450, 560, 703, 867, 1080, 1324, 1633, 1993, 2441, 2960, 3604, 4350, 5262, 6324, 7610, 9104, 10905, 12993, 15490, 18390, 21835, 25825, 30550, 36013, 42445, 49880, 58595

Offset

1,2

Comments

Case k=12,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(11*n/3)/5) * ((11*(3 - sqrt(5)))/30)^(1/4) / (10 * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 5-25))*(1 - x^(25*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035974 A035983 A035993 * A027339 A039837 A039838

Adjacent sequences: A036001 A036002 A036003 * A036005 A036006 A036007

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved