

A222417


Irregular triangle read by rows: row n gives list Q(n) of LCMs of "arrayadmissible" 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
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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 PerronFrobenius theory. Cambridge Tracts in Mathematics, 189. Cambridge University Press, Cambridge, 2012. xii+323 pp. ISBN: 9780521898812 MR2953648
Nussbaum, Roger D.; Scheutzow, Michael. Admissible arrays and a nonlinear generalization of PerronFrobenius theory. J. London Math. Soc. (2) 58 (1998), no. 3, 526544. MR1678149 (2000b:37013)
Nussbaum, R. D.; Verduyn Lunel, S. M. Generalizations of the PerronFrobenius 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 nonexpansive maps, Ergodic Theory Dynam. Systems 23 (2003), no. 4, 11991226. 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
Adjacent sequences: A222414 A222415 A222416 * A222418 A222419 A222420


KEYWORD

nonn,tabf


AUTHOR

N. J. A. Sloane, Feb 28 2013


STATUS

approved



