OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3, -2, 0, 0, 0, 0, 0, 0, -1, 1).
FORMULA
G.f.: (1-x+x^9)/(1-3*x+2*x^2+x^9-x^10).
EXAMPLE
a(10) = 1023 = 2^10-1, because 1000000001 is the only binary word of length 10 with not less than 8 0-digits between any pair of consecutive 1-digits.
MAPLE
a:= n-> (Matrix([[2, 1$9]]). Matrix(10, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$6, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..35);
MATHEMATICA
CoefficientList[Series[(1 - x + x^9) / (1 - 3 x + 2 x^2 + x^9 - x^10), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 02 2008
STATUS
approved