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A035971
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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.
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0
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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
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OFFSET
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1,3
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COMMENTS
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Case k=9,i=2 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) * sin(2*Pi/19) / (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+ 2-19))*(1 - x^(19*k- 2))/(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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