OFFSET
0,10
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,0,-1,0,0,0,0,0,-1).
FORMULA
G.f.: x^8/((x^7+x-1)*(x^8+x-1)).
a(n) = 2*a(n-1) - a(n-2) + a(n-7) - a(n-9) - a(n-15). - Vincenzo Librandi, Jun 05 2013
EXAMPLE
a(9)=2 because 2 binary words of length 9 have at least one subword 10^{6}1 and no subwords 10^{i}1 with i<6: 010000001, 100000010.
MAPLE
a:= n-> coeff(series(x^8/((x^7+x-1)*(x^8+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);
MATHEMATICA
CoefficientList[Series[x^8 / ((x^7 + x - 1) (x^8 + x - 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 04 2013 *)
PROG
(Magma) [n le 8 select 0 else n le 15 select n-8 else 2*Self(n-1)-Self(n-2) +Self(n-7)-Self(n-9)-Self(n-15): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 04 2008
STATUS
approved