OFFSET
0,9
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,0,-1,0,0,0,0,-1).
FORMULA
G.f.: x^7/((x^6+x-1)*(x^7+x-1)).
a(n) = 2*a(n-1) -a(n-2) +a(n-6) -a(n-8) -a(n-13). - Vincenzo Librandi, Jun 05 2013
EXAMPLE
a(8)=2 because 2 binary words of length 8 have at least one subword 1000001 and no subwords 10^{i}1 with i<5: 01000001, 10000010.
MAPLE
a:= n-> coeff(series(x^7/((x^6+x-1)*(x^7+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);
MATHEMATICA
CoefficientList[Series[x^7 / ((x^6 + x - 1) (x^7 + x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 04 2013 *)
PROG
(Magma) [n le 7 select 0 else n le 13 select n-7 else 2*Self(n-1)-Self(n-2) +Self(n-6)-Self(n-8)-Self(n-13): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 04 2008
STATUS
approved