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A164408
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Number of binary strings of length n with no substrings equal to 0000 0001 or 0011.
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2
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1, 2, 4, 8, 13, 23, 40, 68, 118, 203, 349, 602, 1036, 1784, 3073, 5291, 9112, 15692, 27022, 46535, 80137, 138002, 237652, 409256, 704773, 1213679, 2090056, 3599252, 6198214, 10673843, 18381253, 31654058, 54510940, 93872408, 161656153, 278385443, 479403064
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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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G.f.: (x+1)*(x^2+1) / ( 1-x-x^2-x^3+x^4 ). - R. J. Mathar, Nov 28 2011
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MATHEMATICA
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CoefficientList[Series[(13 + 10*x + 4*x^2 - 8*x^3)/(1 - x - x^2 - x^3 + x^4), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jan 10 2017 *)
LinearRecurrence[{1, 1, 1, -1}, {13, 23, 40, 68}, 50] (* G. C. Greubel, Sep 19 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec(x^4*(13+10*x+4*x^2-8*x^3)/(1-x-x^2-x^3+x^4)) \\ G. C. Greubel, Sep 19 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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