A145115 Numbers of length n binary words with fewer than 7 0-digits between any pair of consecutive 1-digits.

1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1019, 2031, 4047, 8063, 16063, 31999, 63743, 126976, 252934, 503838, 1003630, 1999198, 3982334, 7932670, 15801598, 31476221, 62699509, 124895181, 248786733, 495574269, 987166205, 1966399741, 3916997885, 7802519550

Offset: 0

Author

Alois P. Heinz, Oct 02 2008

Keywords

• nonn
• easy

Examples

			a(9) = 511 = 2^9-1, because 100000001 is the only binary word of length 9 with not less than 7 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, -1, 1).

Crossrefs

7th column of A145111.

Programs

Maple

a:= n-> (Matrix([[2, 1$8]]). Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$5, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..35);

Mathematica

CoefficientList[Series[(1 - x + x^8) / (1 - 3 x + 2 x^2 + x^8 - x^9), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)

Formula

G.f.: (1-x+x^8)/(1-3*x+2*x^2+x^8-x^9).