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A005272
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Number of Van Lier sequences of length n.
(Formerly M1682)
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0
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OFFSET
| 2,2
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COMMENTS
| Fishburn's Abstract: We study two types of sequences of positive integers which arise from problems in the measurement of comparative judgements of probability. The first type consists of the Van Lier sequences, which are nondecreasing sequences x_1, x_2,...x_n of positive integers that start with two 1's and have the property that, whenever j<kless than or equal to n, x_k-x_j can be expressed as a sum of terms from the sequence other than x_j. The second type consists of the regular sequences, which are nondecreasing sequences of positive integers that start with two 1's and have the property that each subsequent term is a partial sum of preceding terms. We also study one-term extensions of Van Lier sequences and obtain some asymptotic results on the number of Van Lier sequences. [Jonathan Vos Post, Apr 16, 2011]
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REFERENCES
| P. C. Fishburn et al., Van Lier sequences, Discrete Appl. Math., 27 (1990), 209-220.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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CROSSREFS
| Sequence in context: A047863 A180349 A141713 * A178089 A002449 A059430
Adjacent sequences: A005269 A005270 A005271 * A005273 A005274 A005275
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KEYWORD
| nonn,nice,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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