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A035975
Number of partitions of n into parts not of the form 19k, 19k+6 or 19k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 8 are greater than 1.
0
1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 85, 112, 144, 186, 236, 301, 378, 477, 594, 741, 916, 1134, 1391, 1708, 2083, 2540, 3079, 3732, 4500, 5424, 6508, 7803, 9321, 11125, 13231, 15723, 18628, 22048, 26024, 30688, 36097, 42419, 49736, 58254
OFFSET
1,2
COMMENTS
Case k=9,i=6 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(7*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 6-19))*(1 - x^(19*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A035967 A097797 A219601 * A035984 A035994 A036005
KEYWORD
nonn,easy
STATUS
approved