A036009 Number of partitions of n into parts not of the form 25k, 25k+10 or 25k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 11 are greater than 1.

1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 75, 98, 130, 168, 219, 280, 360, 455, 578, 725, 910, 1132, 1410, 1740, 2149, 2636, 3232, 3940, 4801, 5819, 7050, 8503, 10245, 12298, 14749, 17625, 21042, 25045, 29776, 35305, 41815, 49400, 58300, 68648

Offset

1,2

Comments

Case k=12,i=10 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..45.

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+10-25))*(1 - x^(25*k-10))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A035998 A137792 A039905 * A261776 A027344 A184645

Adjacent sequences: A036006 A036007 A036008 * A036010 A036011 A036012

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved