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A035977
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Number of partitions of n into parts not of the form 19k, 19k+8 or 19k-8. Also number of partitions with at most 7 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, 11, 15, 21, 29, 40, 52, 71, 92, 121, 156, 202, 256, 328, 412, 520, 649, 811, 1002, 1243, 1526, 1875, 2289, 2794, 3388, 4112, 4960, 5982, 7183, 8619, 10299, 12302, 14638, 17404, 20630, 24431, 28848, 34038, 40053, 47088, 55234
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OFFSET
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1,2
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COMMENTS
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Case k=9,i=8 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(3*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+ 8-19))*(1 - x^(19*k- 8))/(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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