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A035971 Number of partitions of n into parts not of the form 19k, 19k+2 or 19k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 8 are greater than 1. 0
1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, 45, 58, 75, 96, 120, 153, 191, 239, 297, 368, 453, 559, 683, 834, 1015, 1233, 1489, 1800, 2164, 2599, 3112, 3720, 4432, 5278, 6262, 7422, 8777, 10365, 12208, 14368, 16869, 19783, 23157, 27073, 31591, 36831 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Case k=9,i=2 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
LINKS
FORMULA
a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * sin(2*Pi/19) / (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+ 2-19))*(1 - x^(19*k- 2))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A105782 A035956 A035963 * A035980 A035990 A036001
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)