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A193316
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Number of basic forbidden patterns of length n of the map f(x)=4x(1-x) on the unit interval.
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0
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OFFSET
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1,4
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COMMENTS
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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].
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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