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A230127
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Number of binary strings of length n avoiding "squares" (that is, repeated blocks of the form xx) with |x| > 1.
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5
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1, 2, 4, 8, 12, 20, 26, 38, 42, 52, 56, 56, 48, 42, 32, 22, 10, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,2
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COMMENTS
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Entringer et al. showed that a(n) = 0 for all n >= 19.
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LINKS
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EXAMPLE
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a(4) = 12 because there are 16 binary strings of length 4, but 4 of these strings (namely 0000, 0101, 1010, and 1111) repeat a substring of length 2. Thus a(4) = 16 - 4 = 12.
a(18) = 2 because there are 2 strings of length 18 not containing any "squares" of length greater than 1: 010011000111001101 and 101100111000110010.
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MATHEMATICA
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a[n_] := a[n] = Select[PadLeft[#, n]& /@ IntegerDigits[Range[0, 2^n-1], 2], {} == SequencePosition[#, {b__, b__} /; Length[{b}]>1, 1]&] // Length;
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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