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1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 4, 4, 8, 6, 10, 11, 13, 15, 22, 20, 28, 33, 39, 43, 58, 60, 77, 88, 104, 119, 148, 160, 197, 226, 265, 300, 363, 404, 481, 549, 638, 727, 858, 961, 1126, 1283, 1480, 1680, 1953, 2201, 2544, 2887, 3309, 3750, 4312, 4857, 5566, 6301, 7175
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OFFSET
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6,7
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COMMENTS
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a(n) counts partitions of n such that all parts are >=2 and the largest part occurs at least three times, see example.
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LINKS
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FORMULA
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a(n) = p(n)-2*p(n-1)+2*p(n-3)-p(n-4), where p(n) = A000041(n).
G.f.: (1-x)*Product_{k>2} 1/(1-x^k). (End)
a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (36*sqrt(2)*n^(5/2)). - Vaclav Kotesovec, Jun 02 2018
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EXAMPLE
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For n = 19 the a(19)=6 partitions are 5554, 44443, 55522, 444322, 3333322, and 33322222.
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MATHEMATICA
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Table[PartitionsP[n] - 2 PartitionsP[n - 1] + 2 PartitionsP[n - 3] - PartitionsP[n - 4], {n, 6, 70}] (* Vincenzo Librandi, Dec 09 2014 *)
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PROG
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(Magma) a:=func<n | NumberOfPartitions(n)-2*NumberOfPartitions(n-1)+2*NumberOfPartitions(n-3)-NumberOfPartitions(n-4)>; [a(n): n in [6..100]]; // Vincenzo Librandi, Dec 09 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Keyword:tabf removed, indexing corrected, sequence extended by R. J. Mathar, Sep 17 2009
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STATUS
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approved
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