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A234591
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Number of binary words of length n which have no 0^b 1 1 0^a 1 0 1 0^b - matches, where a=1, b=2.
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2
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1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2044, 4084, 8160, 16304, 32576, 65088, 130048, 259841, 519173, 1037329, 2072626, 4141192, 8274272, 16532336, 33032288, 65999871, 131870458, 263482601, 526449078, 1051866919, 2101673384, 4199229896, 8390234112
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,0,0,-1,1,1).
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FORMULA
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MAPLE
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a:= n-> coeff(series(-(x^9+x^8+1)/(x^10+x^9-x^8+2*x-1), x, n+1), x, n):
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MATHEMATICA
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a[n_ /; n<=9]:= 2^n; a[n_]:=a[n] =2*a[n-1] -a[n-8] +a[n-9] +a[n-10]; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Mar 18 2014 *)
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PROG
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(PARI) my(x='x+O('x^40)); Vec((1+x^8+x^9)/(1-2*x+x^8-x^9-x^10)) \\ G. C. Greubel, Sep 14 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x^8+x^9)/(1-2*x+x^8-x^9-x^10) )); // G. C. Greubel, Sep 14 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^8+x^9)/(1-2*x+x^8-x^9-x^10)).list()
(GAP) a:=[1, 2, 4, 8, 16, 32, 64, 128, 256, 512];; for n in [11..40] do a[n]:=2*a[n-1]-a[n-8]+a[n-9]+a[n-10]; od; a; # G. C. Greubel, Sep 14 2019
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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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