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A193285
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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.
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3
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%I #17 Mar 02 2020 19:45:32
%S 0,0,0,1,12,89,645,4862,39906,361931,3626663,39912033
%N 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.
%C a(n) is also the number of forbidden patterns of length n of the tent map x -> 1-|1-2x| in [0,1].
%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.
%F a(n) = n! - A193284(n).
%e a(3) = 1 because the only forbidden pattern of length 3 is 321.
%Y Cf. A000142, A193284 (allowed patterns).
%K nonn,more
%O 0,5
%A _Sergi Elizalde_, Jul 20 2011
%E a(0)=0 prepended by _Alois P. Heinz_, Mar 02 2020
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