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,-1,1).
FORMULA
G.f.: (1-x+x^7)/(1-3*x+2*x^2+x^7-x^8).
EXAMPLE
a(8) = 255 = 2^8-1, because 10000001 is the only binary word of length 8 with not less than 6 0-digits between any pair of consecutive 1-digits.
MAPLE
a:= n-> (Matrix([[2, 1$7]]). Matrix(8, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$4, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..35);
MATHEMATICA
CoefficientList[Series[(1 - x + x^7) / (1 - 3 x + 2 x^2 + x^7 - x^8), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{3, -2, 0, 0, 0, 0, -1, 1}, {1, 2, 4, 8, 16, 32, 64, 128}, 40] (* Harvey P. Dale, Mar 13 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 02 2008
STATUS
approved