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 A145113 #19 May 22 2024 02:10:47
%S A145113 1,2,4,8,16,32,64,127,251,495,975,1919,3775,7424,14598,28702,56430,
%T A145113 110942,218110,428797,842997,1657293,3258157,6405373,12592637,
%U A145113 24756478,48669960,95682628,188107100,369808828,727025020,1429293563,2809917167,5524151707
%N A145113 Numbers of length n binary words with fewer than 5 0-digits between any pair of consecutive 1-digits.
%H A145113 Vincenzo Librandi, <a href="/A145113/b145113.txt">Table of n, a(n) for n = 0..1000</a>
%H A145113 T. Langley, J. Liese, and J. Remmel, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Langley/langley2.html">Generating Functions for Wilf Equivalence Under Generalized Factor Order</a>, J. Int. Seq. 14 (2011) # 11.4.2.
%H A145113 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,0,0,-1,1).
%F A145113 G.f.: (1-x+x^6)/(1-3*x+2*x^2+x^6-x^7).
%e A145113 a(7) = 127 = 2^7-1, because 1000001 is the only binary word of length 7 with not less than 5 0-digits between any pair of consecutive 1-digits.
%p A145113 a:= n-> (Matrix([[2, 1$6]]). Matrix(7, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0$3, -1, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);
%t A145113 CoefficientList[Series[(1 - x + x^6) / (1 - 3 x + 2 x^2 + x^6 - x^7), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%Y A145113 5th column of A145111.
%K A145113 nonn,easy
%O A145113 0,2
%A A145113 _Alois P. Heinz_, Oct 02 2008