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A122536
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Number of binary sequences of length n with no initial repeats (or, with no final repeats).
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24
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2, 2, 4, 6, 12, 20, 40, 74, 148, 286, 572, 1124, 2248, 4460, 8920, 17768, 35536, 70930, 141860, 283440, 566880, 1133200, 2266400, 4531686, 9063372, 18124522, 36249044, 72493652, 144987304, 289965744
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OFFSET
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1,1
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COMMENTS
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An initial repeat of a string S is a number k>=1 such that S(i)=S(i+k) for i=0..k-1. In other words, the first k symbols are the same as the next k symbols, e.g., ABCDABCDZQQ has an initial repeat of size 4.
Equivalently, this is the number of binary sequences of length n with curling number 1. See A216955. - N. J. A. Sloane, Sep 26 2012
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LINKS
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FORMULA
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Conjecture: a_n ~ C * 2^n where C is 0.27004339525895354325... [Chaffin, Linderman, Sloane, Wilks, 2012]
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EXAMPLE
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a(4)=6: 0100, 0110, 0111, 1000, 1001 and 1011. (But not 00**, 11**, 0101, 1010.)
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CROSSREFS
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See A121880 for difference from 2^n.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(31)-a(71) computed from recurrence and the first 30 terms of A216958 by N. J. A. Sloane, Sep 28 2012, Oct 25 2012
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STATUS
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approved
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