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A143288 Number of binary words of length n containing at least one subword 10^{8}1 and no subwords 10^{i}1 with i<8.

%I A143288 #15 Oct 12 2018 13:51:31
%S A143288 0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,11,15,21,29,39,51,65,81,99,120,
%T A143288 146,180,225,284,360,456,575,720,895,1106,1362,1676,2065,2550,3156,
%U A143288 3912,4851,6011,7437,9184,11321,13936,17141,21077,25919,31881,39222,48254
%N A143288 Number of binary words of length n containing at least one subword 10^{8}1 and no subwords 10^{i}1 with i<8.
%H A143288 Vincenzo Librandi, <a href="/A143288/b143288.txt">Table of n, a(n) for n = 0..1000</a>
%H A143288 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,-1).
%F A143288 G.f.: x^10/((x^9+x-1)*(x^10+x-1)).
%F A143288 a(n) = A005711(n+7)-A017904(n+19).
%F A143288 a(n) = 2a(n-1) - a(n-2) + a(n-9) - a(n-11) - a(n-19). - _Charles R Greathouse IV_, Jun 04 2013
%e A143288 a(11)=2 because 2 binary words of length 11 have at least one subword 10^{8}1 and no subwords 10^{i}1 with i<8: 01000000001, 10000000010.
%p A143288 a:= n-> coeff(series(x^10/((x^9+x-1)*(x^10+x-1)), x, n+1), x, n):
%p A143288 seq(a(n), n=0..70);
%t A143288 CoefficientList[Series[x^10 / ((x^9 + x - 1) (x^10 + x - 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 04 2013 *)
%t A143288 LinearRecurrence[{2,-1,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,-1},{0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9},60] (* _Harvey P. Dale_, Oct 12 2018 *)
%o A143288 (PARI) Vec(1/((x^9+x-1)(x^10+x-1))+O(x^99)) \\ _Charles R Greathouse IV_, Jun 04 2013
%Y A143288 Cf. A005711, A017904, 8th column of A143291.
%K A143288 nonn,easy
%O A143288 0,12
%A A143288 _Alois P. Heinz_, Aug 04 2008