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

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Last modified July 13 04:01 EDT 2020. Contains 335673 sequences. (Running on oeis4.)