A143289 Number of binary words of length n containing at least one subword 10^{9}1 and no subwords 10^{i}1 with i<9.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 22, 30, 40, 52, 66, 82, 100, 120, 143, 171, 207, 254, 315, 393, 491, 612, 759, 935, 1144, 1392, 1688, 2045, 2480, 3014, 3672, 4483, 5480, 6700, 8185, 9984, 12156, 14774, 17930, 21740, 26349, 31936

Offset

0,13

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: x^11/((x^10+x-1)*(x^11+x-1)).

a(n) = A017904(n+19)-A017905(n+21).

a(n) = 2*a(n-1) -a(n-2) +a(n-10) -a(n-12) -a(n-21). - Vincenzo Librandi, Jun 05 2013

Example

a(12)=2 because 2 binary words of length 12 have at least one subword 10^{9}1 and no subwords 10^{i}1 with i<9: 010000000001, 100000000010.

Maple

a:= n-> coeff(series(x^11/((x^10+x-1)*(x^11+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);

Mathematica

CoefficientList[Series[x^11 / ((x^10 + x - 1) (x^11 + x - 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 05 2013 *)

Prog

(Magma) [n le 11 select 0 else n le 21 select n-11 else 2*Self(n-1)-Self(n-2) +Self(n-10)-Self(n-12)-Self(n-21): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013

Crossrefs

Cf. A017904, A017905, 9th column of A143291.

Sequence in context: A059765 A180479 A193456 * A064807 A235591 A007603

Adjacent sequences: A143286 A143287 A143288 * A143290 A143291 A143292

Keyword

nonn,easy,changed

Author

Alois P. Heinz, Aug 04 2008

Status

approved