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A143281
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Number of binary words of length n containing at least one subword 101 and no subword 11.
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2
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0, 0, 0, 1, 2, 4, 8, 15, 27, 48, 84, 145, 248, 421, 710, 1191, 1989, 3309, 5487, 9073, 14966, 24634, 40472, 66384, 108729, 177858, 290610, 474364, 773615, 1260643, 2052818, 3340662, 5433345, 8832432, 14351403, 23309326, 37844645, 61423513, 99663191, 161665653
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: x^3/((x^2+x-1)*(x^3+x-1)).
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EXAMPLE
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a(6)=8 because 8 binary words of length 6 have at least one substring 101 and no substring 11: 000101, 001010, 010100, 101000, 010101, 101010, 101001, 100101.
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MAPLE
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a:= n-> coeff(series(x^3/((x^2+x-1)*(x^3+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);
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MATHEMATICA
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CoefficientList[Series[x^3/((x^2+x-1)*(x^3+x-1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 28 2017 *)
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PROG
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(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(x^3/((x^2+x-1)*(x^3+x-1)))) \\ G. C. Greubel, Apr 28 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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STATUS
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approved
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