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A164317
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Number of binary strings of length n with no substrings equal to 000, 010, or 111.
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3
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1, 2, 4, 5, 6, 7, 9, 11, 13, 16, 20, 24, 29, 36, 44, 53, 65, 80, 97, 118, 145, 177, 215, 263, 322, 392, 478, 585, 714, 870, 1063, 1299, 1584, 1933, 2362, 2883, 3517, 4295, 5245, 6400, 7812, 9540, 11645, 14212, 17352, 21185, 25857, 31564, 38537, 47042, 57421
(list;
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refs;
listen;
history;
text;
internal format)
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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^2+x+1)*(x^3+2*x^2+x+1)/(x^4+x^3-1). - R. J. Mathar, Nov 28 2011
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EXAMPLE
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All solutions for N=8
00110110 00110011 10110110 10110011 10011001 10011011 01100110 01101100
01101101 11001100 11001101 11011001 11011011
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MATHEMATICA
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CoefficientList[Series[-(x^2 + x + 1) (x^3 + 2 x^2 + x + 1)/(x^4 + x^3 - 1), {x, 0, 50}], x] (* Michael De Vlieger, Feb 17 2020 *)
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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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