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A036032 Number of partitions of n into parts not of form 4k+2, 24k, 24k+7 or 24k-7. Also number of partitions in which no odd part is repeated, with at most 3 parts 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
1, 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 24, 30, 36, 45, 57, 69, 83, 101, 124, 150, 177, 212, 257, 305, 358, 425, 505, 594, 694, 813, 956, 1116, 1293, 1504, 1753, 2029, 2339, 2702, 3123, 3593, 4120, 4729, 5430, 6215, 7090, 8094, 9245, 10525, 11955, 13587 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Case k=6,i=4 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..51.

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 - 17))*(1 - x^(24*k - 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)

CROSSREFS

Sequence in context: A125155 A091179 A036027 * A008813 A133463 A187550

Adjacent sequences:  A036029 A036030 A036031 * A036033 A036034 A036035

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Name corrected by Vaclav Kotesovec, May 09 2018

STATUS

approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)