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A036027
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Number of partitions of n into parts not of form 4k+2, 20k, 20k+7 or 20k-7. Also number of partitions in which no odd part is repeated, with at most 3 parts of size less than or equal to 2 and where differences between parts at distance 4 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, 6, 9, 12, 14, 18, 24, 29, 35, 44, 55, 67, 80, 97, 119, 143, 168, 201, 243, 287, 336, 398, 471, 552, 643, 751, 881, 1025, 1184, 1374, 1597, 1842, 2117, 2440, 2812, 3226, 3689, 4223, 4837, 5520, 6280, 7152, 8148, 9251, 10481, 11883, 13466
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OFFSET
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1,3
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COMMENTS
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Case k=5,i=4 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) ~ exp(Pi*sqrt(2*n/5)) * cos(3*Pi/20) / (10^(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^(4*k - 2))*(1 - x^(20*k))*(1 - x^(20*k+7-20))*(1 - x^(20*k- 7))/(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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EXTENSIONS
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STATUS
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approved
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