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Number of allowed patterns of length n of the map f(x) = 4x(1-x) on the unit interval. A permutation pi is an allowed pattern if there exists x in [0,1] such that the values x,f(x),f(f(x)),...,f^{n-1}(x) are different and in the same relative order as pi_1,pi_2,...,pi_n.
+10
2
1, 1, 2, 5, 12, 31, 75, 178, 414, 949, 2137, 4767
Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=3-e.
+10
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0
Number of basic forbidden patterns of length n of the map f(x)=4x(1-x) on the unit interval.
+10
0
0, 0, 1, 5, 9, 28, 53, 110, 229, 474
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