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A187219
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Number of partitions of n that do not contain parts less than the smallest part of the partitions of n-1.
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64
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1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 137, 165, 210, 253, 320, 383, 478, 574, 708, 847, 1039, 1238, 1507, 1794, 2167, 2573, 3094, 3660, 4378, 5170, 6153, 7245, 8591, 10087, 11914, 13959, 16424, 19196, 22519, 26252, 30701, 35717
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OFFSET
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1,4
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COMMENTS
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Essentially the same as A002865, but here a(1) = 1 not 0.
Also number of regions in the last section of the set of partitions of n.
Also number of partitions of n+k that are formed by k+1 sections, k >= 0 (Cf. A194799). - Omar E. Pol, Jan 30 2012
Also the number of partitions of n with no parts greater than the number of ones. - Spencer Miller, Jan 28 2023
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LINKS
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FORMULA
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EXAMPLE
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Illustration of initial terms as number of regions:
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(End)
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MATHEMATICA
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Join[{1}, Drop[CoefficientList[Series[1 / Product[(1 - x^k)^1, {k, 2, 50}], {x, 0, 50}], x], 2]] (* Vincenzo Librandi, Feb 15 2018 *)
A187219[nmax_]:=Join[{1}, Differences[PartitionsP[Range[nmax]]]];
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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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STATUS
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approved
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