A193316 - OEIS

%I #14 Mar 02 2020 15:07:27

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

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

%C 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.

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

%H S. Elizalde and Y. Liu, <a href="http://arxiv.org/abs/0909.2277v1">On basic forbidden patterns of functions</a>, arXiv:0909.2277 [math.CO], 2009.

%H S. Elizalde and Y. Liu, <a href="https://doi.org/10.1016/j.dam.2011.04.012">On basic forbidden patterns of functions</a>, Discrete Appl. Math. 159 (2011), 1207-1216.

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

%e a(4) = 5 because the basic forbidden patterns of length 4 are 1423, 2134, 2143, 3142, 4231.

%Y Cf. A193284, A193285.

%K nonn,more

%O 1,4

%A _Sergi Elizalde_, Jul 22 2011