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A035952
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Number of partitions of n into parts not of the form 13k, 13k+4 or 13k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 5 are greater than 1.
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5
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1, 2, 3, 4, 6, 9, 12, 17, 22, 30, 39, 52, 66, 86, 109, 139, 174, 220, 272, 340, 419, 517, 632, 775, 940, 1144, 1381, 1668, 2002, 2406, 2873, 3433, 4082, 4852, 5745, 6801, 8018, 9452, 11105, 13039, 15266, 17864, 20845, 24310, 28284, 32881, 38145
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OFFSET
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1,2
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COMMENTS
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Case k=6,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) ~ sin(4*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-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-5)) * (1 - x^(13*k-6)) * (1 - x^(13*k-7)) * (1 - x^(13*k-8)) * (1 - x^(13*k-10)) * (1 - x^(13*k-11)) * (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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