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A108711
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Number of partitions of n with Floor(2n/3) parts.
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0
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1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 7, 11, 11, 11, 15, 15, 15, 22, 22, 22, 30, 30, 30, 42, 42, 42, 56, 56, 56, 77, 77, 77, 101, 101, 101, 135, 135, 135, 176, 176, 176, 231, 231, 231, 297, 297, 297, 385, 385, 385, 490, 490, 490, 627, 627, 627, 792, 792, 792, 1002
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| It would be interesting to know whether the sequence continues with runs of length 3 of terms of equal values.
The number of partitions of n with floor(2n/3) = A004523(n) parts equals the number of partitions of n with maximum part floor(2n/3). This leaves n-floor(2n/3) = A002264(n+2) as the sum of all the other parts, with no further restriction since 2n/3 > n/2 remains the largest part for any partition of the remainder. Since A002264 triplicates the integers, this sequence here triplicates the entries of A000041. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2010]
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EXAMPLE
| The partitions of 6 are {{6},{5,1},{4,2},{4,1,1},{3,3},{3,2,1},{3,1,1,1},{2,2,2},{2,2,1,1},{2,1,1,1,1},{1,1,1,1,1,1}}, of which 2 have 4 parts. Thus a(6)=2.
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CROSSREFS
| Cf. A066639.
Sequence in context: A008650 A062051 A179269 * A029059 A035449 A161555
Adjacent sequences: A108708 A108709 A108710 * A108712 A108713 A108714
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Jun 20 2005
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EXTENSIONS
| a(1) corrected and sequence extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2010
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