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Search: id:A119620
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| A119620 |
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Number of partitions of Floor[3n/2] into n parts each from {1,2,...,n}. |
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+0
1
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| 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 11, 11, 15, 15, 22, 22, 30, 30, 42, 42, 56, 56, 77, 77, 101, 101, 135, 135, 176, 176, 231, 231, 297, 297, 385, 385, 490, 490, 627, 627, 792, 792, 1002, 1002, 1255, 1255, 1575, 1575, 1958, 1958, 2436, 2436, 3010, 3010, 3718, 3718
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The bisection {1,1,2,3,5,7,11,15,22,...} agrees with the initial terms of A008641, Number of partitions of n into at most 12 parts and also A008635, Molien series for A_12.
a(2n+1)=a(2n) for all n>0. Iff the partition {...,1} is a member of a(2n) then the partition {...,1,1} is a member of a(2n+1). - Robert G. Wilson v (rgwv(at)rgwv.com), Jun 09 2006
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FORMULA
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a(n) = A000041(floor(n/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 10 2006
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EXAMPLE
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For n=8, Floor[3n/2] is 12 and there are five partitions of 12 into 8 parts each in the range 1-8 inclusive, namely: {5,1,1,1,1,1,1,1}, {4,2,1,1,1,1,1,1}, {3,3,1,1,1,1,1,1}, {3,2,2,1,1,1,1,1} and {2,2,2,2,1,1,1,1}. Thus a(8)=5.
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MATHEMATICA
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(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := f[n] = Length@ Select[ Partitions[ Floor[3n/2], n], Length@# == n &]; Table[ If[n > 1, f[2Floor[n/2]], f[n]], {n, 57}] (* or *) - Robert G. Wilson v (rgwv(at)rgwv.com), Jun 09 2006
Table[ PartitionsP[ Floor[n/2]], {n, 57}] - Robert G. Wilson v (rgwv(at)rgwv.com), Jun 09 2006
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CROSSREFS
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Cf. A000041, A008641, A008635.
Sequence in context: A040039 A008667 A109763 this_sequence A029018 A096765 A025147
Adjacent sequences: A119617 A119618 A119619 this_sequence A119621 A119622 A119623
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jun 07 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jun 09 2006
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