%I A145115
%S A145115 1,2,4,8,16,32,64,128,256,511,1019,2031,4047,8063,16063,31999,63743,
%T A145115 126976,252934,503838,1003630,1999198,3982334,7932670,15801598,31476221,
%U A145115 62699509,124895181,248786733,495574269,987166205,1966399741,3916997885
%N A145115 Numbers of length n binary words with fewer than 7 0-digits between any 
               pair of consecutive 1-digits.
%F A145115 G.f.: (1-x+x^8)/(1-3*x+2*x^2+x^8-x^9).
%e A145115 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.
%p A145115 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);
%Y A145115 7th column of A145111.
%Y A145115 Sequence in context: A097000 A054046 A008861 this_sequence A104144 A123464 
               A113019
%Y A145115 Adjacent sequences: A145112 A145113 A145114 this_sequence A145116 A145117 
               A145118
%K A145115 nonn
%O A145115 0,2
%A A145115 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 02 2008