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A036029 Number of partitions of n into parts not of form 4k+2, 24k, 24k+1 or 24k-1. Also number of partitions in which no odd part is repeated, with no part of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even. 0
0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 5, 7, 7, 8, 12, 15, 16, 19, 25, 31, 35, 40, 50, 62, 69, 80, 99, 117, 133, 154, 184, 217, 247, 283, 335, 391, 443, 507, 593, 685, 776, 886, 1024, 1175, 1331, 1510, 1733, 1980, 2232, 2526, 2883, 3271, 3682, 4154, 4710, 5324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Case k=6,i=1 of Gordon/Goellnitz/Andrews Theorem.

REFERENCES

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

a(n) ~ 5^(1/4) * sqrt(2 - sqrt(2 + sqrt(3))) * exp(sqrt(5*n/3)*Pi/2) / (8 * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 09 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(24*k))*(1 - x^(24*k - 23))*(1 - x^(24*k - 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)

CROSSREFS

Sequence in context: A000025 A036020 A036024 * A181530 A035362 A042957

Adjacent sequences:  A036026 A036027 A036028 * A036030 A036031 A036032

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)