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A356959
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Number of length-n binary strings that can be infinitely extended to the right to form an overlap-free string.
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0
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2, 4, 6, 10, 14, 18, 22, 26, 32, 36, 40, 44, 48, 52, 58, 64, 72, 76, 80, 84, 88, 92, 98, 102, 106, 110, 114, 120, 128, 134, 142, 150, 160, 164, 168, 172, 176, 180, 186, 190, 194, 198, 202, 208, 216, 220, 228, 232, 236, 240, 244, 248, 252, 258, 266, 274, 284
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OFFSET
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1,1
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COMMENTS
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A binary string is overlap-free if it contains no block of the form axaxa, where a in {0,1} and x a possibly empty string.
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LINKS
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FORMULA
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a(n) = Theta(n^c), where c = 1.15501186367066470321... .
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EXAMPLE
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For example, 010011001011010010 is infinitely extendable to the right, but 010011001011010011 is not (every extension by a word of length 7 gives an overlap).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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