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A164396
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Number of binary strings of length n with no substrings equal to 0001 or 0110.
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1
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1, 2, 4, 8, 14, 24, 41, 70, 120, 205, 350, 597, 1018, 1736, 2960, 5047, 8605, 14671, 25013, 42645, 72706, 123957, 211335, 360306, 614287, 1047300, 1785545, 3044181, 5190033, 8848502, 15085836, 25719884, 43849902, 74759820, 127458225, 217303882
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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-3) + a(n-5) - a(n-6). - Andrew Howroyd, Feb 14 2018
G.f.: (1 + x^3 - x^5)/((1 - x)*(1 - x - x^2 - x^5)). - R. J. Mathar, Nov 30 2011
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MATHEMATICA
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LinearRecurrence[{2, 0, -1, 0, 1, -1}, {1, 2, 4, 8, 14, 24}, 50] (* G. C. Greubel, Sep 18 2017 *)
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PROG
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(PARI) Vec((1 + x^3 - x^5)/((1 - x)*(1 - x - x^2 - x^5)) + 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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