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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 23:39 EDT 2021. Contains 346294 sequences. (Running on oeis4.)