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A164426
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Number of binary strings of length n with no substrings equal to 0000 0011 or 0101.
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1
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13, 21, 34, 53, 81, 124, 188, 282, 422, 630, 936, 1387, 2053, 3033, 4473, 6591, 9704, 14274, 20983, 30832, 45283, 66481, 97576, 143181, 210054, 308108, 451874, 662642, 971620, 1424557, 2088498, 3061702, 4488192, 6579052, 9643637, 14135346
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OFFSET
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4,1
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LINKS
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FORMULA
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G.f.: -x^4*(-13-8*x-13*x^2+7*x^3+14*x^4+12*x^5+8*x^6) / ( (x^3+x-1)*(x^4+x^3-1) ). - R. J. Mathar, Dec 01 2011
a(n) = a(n-1) + 2*a(n-3) - a(n-5) - a(n-6) - a(n-7). - Wesley Ivan Hurt, Aug 19 2022
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MATHEMATICA
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LinearRecurrence[{1, 0, 2, 0, -1, -1, -1}, {13, 21, 34, 53, 81, 124, 188}, 40] (* Harvey P. Dale, Feb 06 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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