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A036031
Number of partitions of n into parts not of form 4k+2, 24k, 24k+5 or 24k-5. Also number of partitions in which no odd part is repeated, with at most 2 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, 3, 4, 6, 8, 10, 12, 16, 21, 25, 30, 39, 49, 58, 70, 86, 105, 125, 148, 179, 216, 254, 298, 356, 422, 492, 575, 677, 794, 922, 1069, 1246, 1450, 1672, 1926, 2230, 2574, 2952, 3385, 3890, 4461, 5094, 5810, 6638, 7575, 8609, 9775, 11115, 12619
OFFSET
1,3
COMMENTS
Case k=6,i=3 of Gordon/Goellnitz/Andrews Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
FORMULA
a(n) ~ 5^(1/4) * sqrt(2*sqrt(2) - sqrt(3) + 1) * exp(sqrt(5*n/3)*Pi/2) / (2^(13/4) * 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 - 19))*(1 - x^(24*k - 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)
CROSSREFS
Sequence in context: A036022 A036026 A116494 * A218947 A017818 A228362
KEYWORD
nonn,easy
EXTENSIONS
Name corrected by Vaclav Kotesovec, May 09 2018
STATUS
approved