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A234589
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Expansion of g.f.: (1+x^6+x^7)/(1-2*x+x^6-x^7-x^8).
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1
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1, 2, 4, 8, 16, 32, 64, 128, 255, 508, 1012, 2016, 4016, 8000, 15937, 31749, 63249, 126002, 251016, 500064, 996207, 1984602, 3953641, 7876278, 15690791, 31258536, 62271945, 124055559, 247138286, 492338537, 980816202, 1953940937, 3892559256, 7754593434, 15448376086, 30775607480, 61309875581, 122138964964
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of binary words of length n which have no 00010100-matches.
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LINKS
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MAPLE
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seq(coeff(series((1+x^6+x^7)/(1-2*x+x^6-x^7-x^8), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 13 2019
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MATHEMATICA
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CoefficientList[Series[(1+x^6+x^7)/(1-2*x+x^6-x^7-x^8), {x, 0, 40}], x] (* G. C. Greubel, Sep 13 2019 *)
LinearRecurrence[{2, 0, 0, 0, 0, -1, 1, 1}, {1, 2, 4, 8, 16, 32, 64, 128}, 40] (* Harvey P. Dale, Aug 31 2023 *)
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PROG
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(PARI) my(x='x+O('x^40)); Vec((1+x^6+x^7)/(1-2*x+x^6-x^7-x^8)) \\ G. C. Greubel, Sep 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x^6+x^7)/(1-2*x+x^6-x^7-x^8) )); // G. C. Greubel, Sep 13 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^6+x^7)/(1-2*x+x^6-x^7-x^8)).list()
(GAP) a:=[1, 2, 4, 8, 16, 32, 64, 128];; for n in [9..40] do a[n]:=2*a[n-1]-a[n-6]+a[n-7]+a[n-8]; od; a; # G. C. Greubel, Sep 13 2019
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CROSSREFS
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Similar to but different from A172317.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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