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A164397
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Number of binary strings of length n with no substrings equal to 0001 or 0111.
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2
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1, 2, 4, 8, 14, 24, 41, 68, 112, 184, 300, 488, 793, 1286, 2084, 3376, 5466, 8848, 14321, 23176, 37504, 60688, 98200, 158896, 257105, 416010, 673124, 1089144, 1762278, 2851432, 4613721, 7465164, 12078896, 19544072, 31622980, 51167064, 82790057, 133957134
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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.: -1/((x^2+x+1)*(x^2+x-1)*(x-1)^2). - R. J. Mathar, Nov 30 2011
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MATHEMATICA
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LinearRecurrence[{2, 0, 0, -2, 0, 1}, {14, 24, 41, 68, 112, 184}, 40] (* Harvey P. Dale, Jan 23 2012 *)
CoefficientList[Series[-1 (14 - 4 x - 7 x^2 - 14 x^3 + 4 x^4 + 8 x^5) / ((1 + x + x^2) (x^2 + x - 1) (x - 1)^2), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 19 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec(-x^4*(14-4*x-7*x^2-14*x^3+4*x^4+8*x^5)/( (1+x+x^2)*(x^2+x-1)*(x-1)^2 )) \\ G. C. Greubel, Sep 18 2017
(Magma) I:=[14, 24, 41, 68, 112, 184]; [n le 6 select I[n] else 2*Self(n-1)-2*Self(n-4)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, 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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