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 A005272 Number of Van Lier sequences of length n. (Formerly M1682) 6
 1, 2, 6, 26, 164, 1529, 21439, 461481, 15616226, 851607867, 76555549499, 11550559504086 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS From Fishburn et al.'s abstract (from the 1990 article): "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 < k <= 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Table of n, a(n) for n=2..13. Peter C. Fishburn, Fred S. Roberts, Uniqueness in finite measurement, Applications of combinatorics and graph theory to the biological and social sciences, 103-137, IMA Vol. Math. Appl., 17, Springer, New York, 1989. MR1009374 (90e:92099) Peter C. Fishburn, Fred S. Roberts, Uniqueness in finite measurement, in Applications of combinatorics and graph theory to the biological and social sciences, 103-137, IMA Vol. Math. Appl., 17, Springer, New York, 1989. MR1009374 (90e:92099). [Annotated scan of five pages only] P. C. Fishburn et al., Van Lier Sequences, Discrete Appl. Math. 27 (1990), pp. 209-220. CROSSREFS Sequences in the Fishburn-Roberts (1989) article: A005269, A005268, A234595, A005272, A003513, A008926. Sequence in context: A047863 A180349 A141713 * A307082 A178089 A363003 Adjacent sequences: A005269 A005270 A005271 * A005273 A005274 A005275 KEYWORD nonn,nice,more AUTHOR N. J. A. Sloane EXTENSIONS a(9)-a(10) from Sean A. Irvine, Apr 29 2016 a(11)-a(13) from Bert Dobbelaere, Jan 08 2020 STATUS approved

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Last modified February 27 15:42 EST 2024. Contains 370377 sequences. (Running on oeis4.)