A193316 Number of basic forbidden patterns of length n of the map f(x)=4x(1-x) on the unit interval.

0, 0, 1, 5, 9, 28, 53, 110, 229, 474

Offset

1,4

Comments

A permutation pi is a forbidden pattern if there is no x in [0,1] such that the values x,f(x),f(f(x)),...,f^{n-1}(x) are in the same relative order as pi_1,pi_2,...,pi_n. A forbidden pattern is basic if it is minimally forbidden, that is, the patterns obtained by removing pi_1 or pi_n are not forbidden.

a(n) is also the number of basic forbidden patterns of length n of the tent map x -> 1-|1-2x| in [0,1].

Links

Table of n, a(n) for n=1..10.

S. Elizalde and Y. Liu, On basic forbidden patterns of functions, arXiv:0909.2277 [math.CO], 2009.

S. Elizalde and Y. Liu, On basic forbidden patterns of functions, Discrete Appl. Math. 159 (2011), 1207-1216.

Example

a(3) = 1 because the only basic forbidden pattern of length 3 is 321.
a(4) = 5 because the basic forbidden patterns of length 4 are 1423, 2134, 2143, 3142, 4231.

Crossrefs

Cf. A193284, A193285.

Sequence in context: A272287 A272315 A301747 * A026587 A147367 A147230

Adjacent sequences: A193313 A193314 A193315 * A193317 A193318 A193319

Keyword

nonn,more

Author

Sergi Elizalde, Jul 22 2011

Status

approved