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A143290 Number of binary words of length n containing at least one subword 10^{10}1 and no subwords 10^{i}1 with i<10. 2

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,13,17,23,31,41,53,67,

%T 83,101,121,143,168,198,236,285,348,428,528,651,800,978,1188,1434,

%U 1722,2061,2464,2948,3534,4247,5116,6174,7458,9009,10873,13103,15762,18927

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

%H Vincenzo Librandi, <a href="/A143290/b143290.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: x^12/((x^11+x-1)*(x^12+x-1)).

%F a(n) = A017905(n+21)-A017906(n+23).

%F a(n) = 2*a(n-1) -a(n-2) +a(n-11) -a(n-13) -a(n-23). - _Vincenzo Librandi_, Jun 05 2013

%e a(13)=2 because 2 binary words of length 13 have at least one subword 10^{10}1 and no subwords 10^{i}1 with i<10: 0100000000001, 1000000000010.

%p a:= n-> coeff(series(x^12/((x^11+x-1)*(x^12+x-1)), x, n+1), x, n):

%p seq(a(n), n=0..60);

%t CoefficientList[Series[x^12 / ((x^11 + x - 1) (x^12 + x - 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 05 2013 *)

%o (MAGMA) [n le 12 select 0 else n le 23 select n-12 else 2*Self(n-1)-Self(n-2) +Self(n-11)-Self(n-13)-Self(n-23): n in [1..60]]; // _Vincenzo Librandi_, Jun 05 2013

%Y Cf. A017905, A017906, 10th column of A143291.

%K nonn,easy

%O 0,14

%A _Alois P. Heinz_, Aug 04 2008

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Last modified November 12 05:52 EST 2019. Contains 329051 sequences. (Running on oeis4.)