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A035954
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Number of partitions of n into parts not of the form 13k, 13k+6 or 13k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 5 are greater than 1.
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6
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1, 1, 2, 3, 5, 7, 10, 13, 19, 25, 34, 44, 59, 75, 98, 124, 159, 199, 252, 312, 391, 481, 595, 727, 893, 1084, 1320, 1594, 1928, 2315, 2784, 3325, 3977, 4730, 5627, 6664, 7894, 9310, 10981, 12905, 15162, 17756, 20787, 24263, 28310, 32946, 38317, 44462
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OFFSET
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0,3
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COMMENTS
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Case k=6,i=6 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(6*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; CoefficientList[Series[Product[1 / ((1 - x^(13*k-1)) * (1 - x^(13*k-2)) * (1 - x^(13*k-3)) * (1 - x^(13*k-4)) * (1 - x^(13*k-5)) * (1 - x^(13*k-8)) * (1 - x^(13*k-9)) * (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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EXTENSIONS
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STATUS
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approved
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