This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A145114 #8 Mar 13 2023 15:09:07
%S A145114 1,2,4,8,16,32,64,128,255,507,1007,1999,3967,7871,15615,30976,61446,
%T A145114 121886,241774,479582,951294,1886974,3742973,7424501,14727117,
%U A145114 29212461,57945341,114939389,227991805,452240638,897056776,1779386436,3529560412,7001175484
%N A145114 Numbers of length n binary words with fewer than 6 0-digits between any pair of consecutive 1-digits.
%H A145114 Vincenzo Librandi, <a href="/A145114/b145114.txt">Table of n, a(n) for n = 0..1000</a>
%H A145114 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,0,0,0,-1,1).
%F A145114 G.f.: (1-x+x^7)/(1-3*x+2*x^2+x^7-x^8).
%e A145114 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.
%p A145114 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);
%t A145114 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 *)
%t A145114 LinearRecurrence[{3,-2,0,0,0,0,-1,1},{1,2,4,8,16,32,64,128},40] (* _Harvey P. Dale_, Mar 13 2023 *)
%Y A145114 6th column of A145111.
%K A145114 nonn,easy
%O A145114 0,2
%A A145114 _Alois P. Heinz_, Oct 02 2008