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A234592
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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=b=2.
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2
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1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2047, 4092, 8180, 16352, 32688, 65344, 130624, 261120, 521984, 1043457, 2085893, 4169745, 8335410, 16662664, 33309024, 66585456, 133105760, 266081280, 531902207, 1063283962, 2125527529, 4248975286, 8493793063
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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 (2,0,0,0,0,0,0,0,-1,1,1).
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FORMULA
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G.f.: (1+x^9+x^10)/(1-2*x+x^9-x^10-x^11). - Alois P. Heinz, Jan 08 2014
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MAPLE
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a:= n-> coeff(series(-(x^10+x^9+1)/(x^11+x^10-x^9+2*x-1), x, n+1), x, n):
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MATHEMATICA
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a[n_ /; n<=10]:= 2^n; a[n_]:=a[n] =2*a[n-1] -a[n-9] +a[n-10] +a[n-11]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 18 2014 *)
LinearRecurrence[{2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1}, {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024}, 40] (* Harvey P. Dale, May 17 2018 *)
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PROG
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(PARI) my(x='x+O('x^40)); Vec((1+x^9+x^10)/(1-2*x+x^9-x^10-x^11)) \\ G. C. Greubel, Sep 14 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x^9+x^10)/(1-2*x+x^9-x^10-x^11) )); // G. C. Greubel, Sep 14 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^9+x^10)/(1-2*x+x^9-x^10-x^11)).list()
(GAP) a:=[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024];; for n in [12..40] do a[n]:=2*a[n-1]-a[n-9]+a[n-10]+a[n-11]; 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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