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A036034
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Number of partitions of n into parts not of form 4k+2, 24k, 24k+11 or 24k-11. Also number of partitions in which no odd part is repeated, with at most 5 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.
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0
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1, 1, 2, 3, 4, 5, 7, 10, 13, 16, 20, 27, 33, 40, 51, 64, 78, 94, 115, 141, 170, 202, 243, 294, 349, 411, 489, 581, 683, 800, 940, 1105, 1290, 1498, 1745, 2034, 2355, 2718, 3145, 3636, 4184, 4804, 5520, 6340, 7258, 8289, 9472, 10821, 12324, 14011, 15935
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OFFSET
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1,3
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COMMENTS
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Case k=6,i=6 of Gordon/Goellnitz/Andrews Theorem.
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REFERENCES
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G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
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LINKS
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FORMULA
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a(n) ~ 5^(1/4) * sqrt(2 + sqrt(2 + sqrt(3))) * exp(sqrt(5*n/3)*Pi/2) / (8 * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 09 2018
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MATHEMATICA
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nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(24*k))*(1 - x^(24*k - 13))*(1 - x^(24*k - 11))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 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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EXTENSIONS
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STATUS
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approved
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