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A036028
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Number of partitions of n into parts not of form 4k+2, 20k, 20k+9 or 20k-9. Also number of partitions in which no odd part is repeated, with at most 4 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, 7, 10, 12, 15, 19, 25, 31, 37, 47, 59, 71, 85, 104, 127, 152, 180, 216, 260, 307, 360, 427, 506, 592, 690, 809, 948, 1101, 1274, 1480, 1719, 1983, 2281, 2631, 3033, 3477, 3979, 4560, 5221, 5957, 6782, 7729, 8804, 9995, 11329, 12850
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OFFSET
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1,3
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COMMENTS
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Case k=5,i=5 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(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+9-20))*(1 - x^(20*k- 9))/(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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