A193285 Number of forbidden patterns of length n of the map f(x) = 4x(1-x) on the unit interval. 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.

0, 0, 0, 1, 12, 89, 645, 4862, 39906, 361931, 3626663, 39912033

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..11.

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

Formula

a(n) = n! - A193284(n).

Example

a(3) = 1 because the only forbidden pattern of length 3 is 321.

Crossrefs

Cf. A000142, A193284 (allowed patterns).

Sequence in context: A083825 A181944 A359311 * A199558 A034197 A217089

Adjacent sequences: A193282 A193283 A193284 * A193286 A193287 A193288

Keyword

nonn,more

Author

Sergi Elizalde, Jul 20 2011

Extensions

a(0)=0 prepended by Alois P. Heinz, Mar 02 2020

Status

approved