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A035975
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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.
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0
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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
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OFFSET
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1,2
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COMMENTS
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Case k=9,i=6 of Gordon Theorem.
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REFERENCES
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G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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