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A072380
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Third differences of partition numbers A000041.
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10
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-1, 1, -1, 2, -2, 3, -2, 3, -2, 5, -4, 7, -3, 7, -3, 11, -5, 15, -4, 17, -2, 24, -4, 32, 1, 38, 5, 53, 7, 70, 18, 86, 33, 115, 45, 152, 74, 191, 109, 254, 150, 331, 218, 420, 307, 551, 410, 716, 567, 913, 767, 1186, 1015, 1529, 1358, 1951, 1799, 2513, 2344, 3222, 3079, 4096, 4009, 5237, 5173
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OFFSET
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0,4
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COMMENTS
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Comtet appears to say this is nonnegative, which is only true for n sufficiently large.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115.
A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (72 * sqrt(2) * n^(5/2)). - Vaclav Kotesovec, Oct 06 2017
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MATHEMATICA
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Differences[PartitionsP[Range[0, 70]], 3] (* Harvey P. Dale, Aug 16 2012 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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