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A035966
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Number of partitions of n into parts not of the form 17k, 17k+5 or 17k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 7 are greater than 1.
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0
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1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 61, 78, 103, 131, 170, 213, 273, 340, 429, 531, 663, 814, 1008, 1230, 1509, 1833, 2233, 2695, 3264, 3921, 4719, 5644, 6758, 8046, 9590, 11372, 13492, 15942, 18838, 22177, 26110, 30637, 35941, 42043, 49162
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OFFSET
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1,2
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COMMENTS
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Case k=8,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(2*Pi*sqrt(7*n/51)) * 7^(1/4) * cos(7*Pi/34) / (3^(1/4) * 17^(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^(17*k))*(1 - x^(17*k+ 5-17))*(1 - x^(17*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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