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 A145116 #8 May 23 2024 09:40:57
%S A145116 1,2,4,8,16,32,64,128,256,512,1023,2043,4079,8143,16255,32447,64767,
%T A145116 129279,258047,515072,1028102,2052126,4096110,8175966,16319486,
%U A145116 32574206,65019134,129780222,259045373,517062645,1032073165,2060050221,4111924477,8207529469
%N A145116 Numbers of length n binary words with fewer than 8 0-digits between any pair of consecutive 1-digits.
%H A145116 Vincenzo Librandi, <a href="/A145116/b145116.txt">Table of n, a(n) for n = 0..1000</a>
%H A145116 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, 0, 0, 0, 0, 0, 0, -1, 1).
%F A145116 G.f.: (1-x+x^9)/(1-3*x+2*x^2+x^9-x^10).
%e A145116 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.
%p A145116 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);
%t A145116 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 *)
%Y A145116 8th column of A145111.
%K A145116 nonn,easy
%O A145116 0,2
%A A145116 _Alois P. Heinz_, Oct 02 2008