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A035974
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Number of partitions of n into parts not of the form 19k, 19k+5 or 19k-5. Also number of partitions with at most 4 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, 6, 10, 13, 19, 25, 35, 45, 62, 79, 104, 133, 173, 217, 279, 348, 440, 546, 683, 840, 1043, 1275, 1567, 1907, 2328, 2815, 3416, 4111, 4957, 5940, 7125, 8498, 10148, 12055, 14327, 16959, 20075, 23673, 27920, 32816, 38562, 45185, 52923
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OFFSET
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1,2
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COMMENTS
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Case k=9,i=5 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(9*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+ 5-19))*(1 - x^(19*k- 5))/(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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