%I M1682 #41 May 16 2023 08:12:15

%S 1,2,6,26,164,1529,21439,461481,15616226,851607867,76555549499,

%T 11550559504086

%N Number of Van Lier sequences of length n.

%C 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

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Peter C. Fishburn, Fred S. Roberts, <a href="http://dx.doi.org/10.1007/978-1-4684-6381-1_5">Uniqueness in finite measurement</a>, 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)

%H Peter C. Fishburn, Fred S. Roberts, <a href="/A005269/a005269.pdf">Uniqueness in finite measurement</a>, 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]

%H P. C. Fishburn et al., <a href="http://dx.doi.org/10.1016/0166-218X(90)90066-L">Van Lier Sequences</a>, Discrete Appl. Math. 27 (1990), pp. 209-220.

%Y Sequences in the Fishburn-Roberts (1989) article: A005269, A005268, A234595, A005272, A003513, A008926.

%K nonn,nice,more

%O 2,2

%A _N. J. A. Sloane_

%E a(9)-a(10) from _Sean A. Irvine_, Apr 29 2016

%E a(11)-a(13) from _Bert Dobbelaere_, Jan 08 2020