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Search: id:A109509
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| A109509 |
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Number of hierachical orderings with at least 2 elements on each level for n unlabeled elements. Unlabeled analog of A097236. |
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+0
2
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| 1, 0, 1, 1, 3, 4, 9, 14, 28, 47, 88, 152, 279, 486, 876, 1539, 2744, 4824, 8551, 15023, 26503, 46509, 81747, 143210, 251007, 438915, 767403, 1339487, 2336955, 4071906, 7090589, 12333894, 21440241, 37235775, 64624267, 112067176
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A109509 is the Euler transform of the right-shifted Fibonacci numbers A000045.
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LINKS
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N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
Thomas Wieder, Home Page.
Thomas Wieder, (Old) Home Page.
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EXAMPLE
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Let * be an unlabeled element.
Let | be a delimiter between two hierarchies. E.g. for n=3 we have in **|* two hierarchies (each with one level only).
Let : denote a higher level (within a single hierarchy). E.g. for n=6 we have in ***:**:* a single hierarchy distributed over three levels.
Then a(5) = 4 because we have *****, ***:**, **:***, **|***.
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MAPLE
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SeqSetSetxU := [T, {T=Set(S), S=Sequence(U, card>=1), U=Set(Z, card>=2)}, unlabeled]; seq(count(SeqSetSetxU, size=j), j=1..25); # where x is an integer 1, 2, 3, ... # x=2 gives 2 individuals per level.
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PROGRAM
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(PARI) ET(v)=Vec(prod(k=1, #v, 1/(1-x^k+x*O(x^#v))^v[k]))
ET(vector(40, n, fibonacci(n-1)))
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CROSSREFS
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Cf. A075729, A097236, A000045, A166861.
Sequence in context: A007293 A014596 A002823 this_sequence A006053 A051841 A096081
Adjacent sequences: A109506 A109507 A109508 this_sequence A109510 A109511 A109512
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KEYWORD
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nonn
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AUTHOR
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Thomas Wieder (wieder.thomas(AT)t-online.de), Jun 30 2005
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EXTENSIONS
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Edited with more terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 21 2009
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