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, 0, -1, 1).
FORMULA
G.f.: (1-x+x^10)/(1-3*x+2*x^2+x^10-x^11).
EXAMPLE
a(11) = 2047 = 2^11-1, because 10000000001 is the only binary word of length 11 with not less than 9 0-digits between any pair of consecutive 1-digits.
MAPLE
a:= n-> (Matrix([[2, 1$10]]). Matrix(11, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$7, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..35);
MATHEMATICA
CoefficientList[Series[(1 - x + x^10) / (1 - 3 x + 2 x^2 + x^10 - x^11), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{3, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024}, 40] (* Harvey P. Dale, Sep 24 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 02 2008
STATUS
approved