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A222417
Irregular triangle read by rows: row n gives list Q(n) of LCMs of "array-admissible" sets for n.
3
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 12, 1, 2, 3, 4, 5, 6, 7, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 30, 40, 60, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 24, 28, 30, 40, 60
OFFSET
1,3
COMMENTS
See Nussbaum and Verduyn Lunel (1999) and (2003) for precise definition of Q(n). There are in fact several different but equivalent definitions. For example, Q(n) is "intimately connected to the set of periods of periodic points of classes of nonlinear maps defined on the positive cone in R^n" [Nussbaum and Verduyn Lunel (2003)]
REFERENCES
Lemmens, Bas; Nussbaum, Roger. Nonlinear Perron-Frobenius theory. Cambridge Tracts in Mathematics, 189. Cambridge University Press, Cambridge, 2012. xii+323 pp. ISBN: 978-0-521-89881-2 MR2953648
Nussbaum, Roger D.; Scheutzow, Michael. Admissible arrays and a nonlinear generalization of Perron-Frobenius theory. J. London Math. Soc. (2) 58 (1998), no. 3, 526--544. MR1678149 (2000b:37013)
Nussbaum, R. D.; Verduyn Lunel, S. M. Generalizations of the Perron-Frobenius theorem for nonlinear maps. Mem. Amer. Math. Soc.138 (1999), no. 659, viii+98 pp. MR1470912 (99i:58125). Gives the first 50 rows.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..343 [First 17 rows, flattened]
Nussbaum, Roger D.; Verduyn Lunel, Sjoerd M., Asymptotic estimates for the periods of periodic points of non-expansive maps, Ergodic Theory Dynam. Systems 23 (2003), no. 4, 1199--1226. See the function Q(n). MR1997973 (2004m:37033).
EXAMPLE
Triangle begins
[1]
[1, 2]
[1, 2, 3]
[1, 2, 3, 4]
[1, 2, 3, 4, 5, 6]
[1, 2, 3, 4, 5, 6, 12]
[1, 2, 3, 4, 5, 6, 7, 10, 12]
[1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 24]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24]
...
CROSSREFS
Cf. A222422 (maximal elements only), A222801 (number of terms |Q(n)|).
Sequence in context: A256553 A194896 A212721 * A253573 A229945 A119585
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Feb 28 2013
STATUS
approved