A145116 Numbers of length n binary words with fewer than 8 0-digits between any pair of consecutive 1-digits.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2043, 4079, 8143, 16255, 32447, 64767, 129279, 258047, 515072, 1028102, 2052126, 4096110, 8175966, 16319486, 32574206, 65019134, 129780222, 259045373, 517062645, 1032073165, 2060050221, 4111924477, 8207529469

Offset: 0

Author

Alois P. Heinz, Oct 02 2008

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

8th column of A145111.

Programs

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 *)

Formula

G.f.: (1-x+x^9)/(1-3*x+2*x^2+x^9-x^10).