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A164401
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Number of binary strings of length n with no substrings equal to 0010 or 0101.
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1
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1, 2, 4, 8, 14, 25, 45, 81, 146, 264, 477, 861, 1554, 2805, 5063, 9139, 16497, 29779, 53754, 97031, 175150, 316162, 570702, 1030171, 1859556, 3356674, 6059113, 10937270, 19742803, 35637620, 64329263, 116120383, 209608236, 378362622, 682980194, 1232843622
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-2) + a(n-3) + a(n-6). - Andrew Howroyd, Feb 14 2018
G.f.: (1 + x^2 + x^3 + x^5)/(1 - 2*x + x^2 - x^3 - x^6). - R. J. Mathar, Nov 30 2011
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MATHEMATICA
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LinearRecurrence[{2, -1, 1, 0, 0, 1}, {1, 2, 4, 8, 14, 25}, 50] (* G. C. Greubel, Sep 18 2017 *)
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PROG
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(PARI) Vec((1 + x^2 + x^3 + x^5)/(1 - 2*x + x^2 - x^3 - x^6) + O(x^40)) \\ G. C. Greubel, Sep 18 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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