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Search: id:A110045
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| A110045 |
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Number of hierarchical orderings ("societies") of n unlabeled elements ("individuals") with at least two occupied levels. |
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+0
1
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| 1, 0, 1, 3, 8, 18, 45, 102, 245, 565, 1324, 3049, 7066, 16199, 37187, 84887, 193532, 439600, 996818, 2253941, 5086980, 11454778, 25746467, 57756522, 129342179, 289153474, 645399011, 1438308839, 3200671082, 7112360474, 15783402471
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Unlabeled analogue of A097237.
Primes in this sequence include: a(3) = 3, a(11) = 3049, a(19) = 2253941, a(22) = 25746467. Semiprimes in this sequence include: a(9) = 565 = 5 * 113, a(12) = 7066 = 2 * 3533, a(13) = 16199 = 97 * 167, a(14) = 37187 = 41 * 907, a(15) = 84887 = 11 * 7717, a(18) = 996818 = 2 * 498409, a(24) = 129342179 = 23 * 5623573, a(30) = 15783402471 = 3 * 5261134157. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 10 2005
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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 levels of a hierarchy.
Let | be a delimiter between two subhierarchies.
a(4) = 8 because we have *:*:*:*, ***:*, **:*:*, *:*|*:*, *:***, **:**, *:**:*, *:*:**.
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MAPLE
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SetSeqXSetU := [S, {S=Set(U), U=Sequence(V, card>=2), V=Set(Z, card>=1)}, unlabeled]; seq(count(SetSeqXSetU, size=j), j=0..30); #where x is an integer 1, 2, 3, ... # x=2 gives 2 levels per society.
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CROSSREFS
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Cf. A075729, A034691, A097237.
Sequence in context: A026756 A026384 A066143 this_sequence A108931 A032100 A023371
Adjacent sequences: A110042 A110043 A110044 this_sequence A110046 A110047 A110048
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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), Jul 09 2005
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