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A035958
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Number of partitions of n into parts not of the form 15k, 15k+4 or 15k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 6 are greater than 1.
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0
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1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 40, 54, 69, 90, 115, 147, 185, 235, 292, 366, 453, 561, 689, 848, 1033, 1261, 1529, 1853, 2233, 2693, 3227, 3869, 4618, 5507, 6543, 7771, 9194, 10872, 12817, 15096, 17732, 20814, 24365, 28501, 33265, 38786, 45133
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OFFSET
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1,2
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COMMENTS
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Case k=7,i=4 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(2*n/15)) * 2^(1/4) * cos(7*Pi/30) / (15^(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^(15*k))*(1 - x^(15*k+ 4-15))*(1 - x^(15*k- 4))/(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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