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A035950
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Number of partitions of n into parts not of the form 13k, 13k+2 or 13k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 5 are greater than 1.
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0
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1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 25, 34, 43, 55, 70, 89, 111, 140, 173, 215, 265, 326, 397, 487, 590, 715, 863, 1041, 1247, 1497, 1785, 2129, 2530, 3003, 3551, 4200, 4947, 5823, 6837, 8020, 9380, 10967, 12787, 14898, 17322, 20120, 23322, 27018, 31235
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OFFSET
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1,3
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COMMENTS
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Case k=6,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) ~ sin(2*Pi/13) * 5^(1/4) * exp(2*Pi*sqrt(5*n/39)) / (3^(1/4) * 13^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 22 2015
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MATHEMATICA
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nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-9)) * (1 - x^(13*k-10)) * (1 - x^(13*k-12)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 22 2015 *)
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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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