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A036030
Number of partitions of n into parts not of form 4k+2, 24k, 24k+3 or 24k-3. Also number of partitions in which no odd part is repeated, with 1 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
1, 1, 1, 2, 3, 3, 4, 6, 8, 9, 11, 15, 19, 22, 27, 35, 43, 50, 60, 75, 90, 105, 125, 152, 181, 210, 247, 295, 347, 402, 469, 553, 645, 743, 861, 1004, 1162, 1333, 1535, 1776, 2042, 2332, 2670, 3067, 3507, 3989, 4545, 5190, 5905, 6691, 7589, 8621, 9765
OFFSET
1,4
COMMENTS
Case k=6,i=2 of Gordon/Goellnitz/Andrews Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
FORMULA
a(n) ~ 5^(1/4) * (3 - 2*sqrt(2))^(1/4) * exp(sqrt(5*n/3)*Pi/2) / (2^(11/4) * 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 - 21))*(1 - x^(24*k - 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)
CROSSREFS
Sequence in context: A365831 A036021 A036025 * A036022 A036026 A116494
KEYWORD
nonn,easy
EXTENSIONS
Name corrected by Vaclav Kotesovec, May 09 2018
STATUS
approved