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A005268
Number of elementary sequences of length n.
(Formerly M1233)
6
1, 1, 2, 4, 10, 31, 120, 578, 3422, 24504, 208833, 2086777, 24123293, 318800755, 4766262421, 79874304340, 1488227986802, 30607651830459, 690396731660950
OFFSET
1,3
COMMENTS
In Fishburn-Roberts (1989) it is stated that no recurrence is known. - N. J. A. Sloane, Jan 04 2014
From Fishburn et al.'s abstract (from the 1993 article): "Recent research in uniqueness of representability for finite measurement structures has identified a number of novel finite integer sequences. One of the simplest, called an elementary sequence, is a nondecreasing integer sequence x_1,x_2,...,x_n with x_1=x_2=1 and, for all k > 2, if x_k > 1 then x_k=x_i+x_j for distinct i,j < k." - Martin Fuller, Dec 05 2025
REFERENCES
Peter C. Fishburn and 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)
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Peter C. Fishburn and 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]
Peter C. Fishburn and Fred S. Roberts, Elementary sequences, sub-Fibonacci sequences, Discrete Appl. Math. 44 (1993), no. 1-3, 261-281.
CROSSREFS
Sequences in the Fishburn-Roberts (1989) article: A005269, A005268, A234595, A005272, A003513, A008926.
Sequence in context: A328815 A242347 A138415 * A243931 A005269 A070900
KEYWORD
nonn,more
EXTENSIONS
a(11) corrected and a(12)-a(14) from Sean A. Irvine, Apr 27 2016
a(15)-a(17) from Bert Dobbelaere, Dec 28 2020
a(18)-a(19) from Martin Fuller, Dec 05 2025
STATUS
approved