A036005 Number of partitions of n into parts not of the form 25k, 25k+6 or 25k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 146, 189, 241, 308, 388, 491, 614, 768, 953, 1183, 1457, 1794, 2196, 2686, 3268, 3973, 4807, 5812, 6998, 8416, 10087, 12076, 14411, 17177, 20417, 24239, 28703, 33949, 40060, 47217, 55535, 65240

Offset

1,2

Comments

Case k=12,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(11*n/3)/5) * 11^(1/4) * sin(6*Pi/25) / (3^(1/4) * 5^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(25*k))*(1 - x^(25*k+ 6-25))*(1 - x^(25*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035975 A035984 A035994 * A104503 A027340 A000701

Adjacent sequences: A036002 A036003 A036004 * A036006 A036007 A036008

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved