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 A209888 #34 Aug 06 2018 15:12:23
%S A209888 1,2,4,8,16,31,60,116,225,436,845,1637,3172,6146,11909,23075,44711,
%T A209888 86633,167863,325256,630226,1221144,2366125,4584673,8883398,17212733,
%U A209888 33351899,64623621,125216632,242623433,470114310,910907331,1765000872,3419917668,6626533192
%N A209888 Number of binary words of length n containing no subword 01101.
%C A209888 Notice that the proper suffix 01 of 01101 is also a prefix of 01101. If instead of 01101 subword 01011 is not allowed, we get A107066 with A107066(n) < a(n) for all n >= 8. Word 01101101 of length 8 is the smallest binary word having two or more copies of 01101.
%H A209888 Alois P. Heinz, <a href="/A209888/b209888.txt">Table of n, a(n) for n = 0..1000</a>
%H A209888 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,2,-1).
%F A209888 G.f.: (x+1)*(x^2-x+1) / (x^5-2*x^4+x^3-2*x+1).
%F A209888 a(n) = 2^n if n<5, and a(n) = 2*(a(n-1)+a(n-4)) -a(n-3) -a(n-5) otherwise.
%e A209888 a(6) = 60 because among the 2^6 = 64 binary words of length 6 only 4, namely 001101, 011010, 011011 and 101101 contain the subword 01101.
%p A209888 a:= n-> (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5, [-1, 2, -1, 0, 2][j], 0)))^n. <<1, 2, 4, 8, 16>>)[1, 1]: seq(a(n), n=0..40);
%t A209888 CoefficientList[Series[(x + 1)*(x^2 - x + 1)/(x^5 - 2*x^4 + x^3 - 2*x + 1), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Apr 28 2017 *)
%t A209888 LinearRecurrence[{2,0,-1,2,-1},{1,2,4,8,16},40] (* _Harvey P. Dale_, Sep 17 2017 *)
%Y A209888 Column 22 of A209972.
%Y A209888 Column k=0 of A277751.
%Y A209888 Cf. A107066, A317669.
%K A209888 nonn
%O A209888 0,2
%A A209888 _Alois P. Heinz_, Mar 14 2012