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A035973
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Number of partitions of n into parts not of the form 19k, 19k+4 or 19k-4. Also number of partitions with at most 3 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, 4, 6, 9, 12, 17, 23, 31, 41, 55, 71, 93, 119, 153, 194, 247, 309, 389, 484, 602, 743, 918, 1124, 1378, 1679, 2043, 2474, 2995, 3606, 4341, 5204, 6231, 7436, 8866, 10534, 12506, 14804, 17504, 20645, 24325, 28589, 33569, 39332, 46032, 53771
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OFFSET
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1,2
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COMMENTS
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Case k=9,i=4 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(4*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+ 4-19))*(1 - x^(19*k- 4))/(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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