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 A210003 #17 Oct 05 2015 13:29:05
%S A210003 1,2,4,8,16,31,60,116,224,433,837,1618,3128,6047,11690,22599,43688,
%T A210003 84457,163271,315633,610177,1179585,2280356,4408350,8522156,16474904,
%U A210003 31849037,61570080,119026354,230099960,444825787,859930531,1662404788,3213735970,6212746113
%N A210003 Number of binary words of length n containing no subword 10001.
%C A210003 Each of the subwords 10001, 10011, 10111, 11001, 11101 and their binary complements give the same sequence.
%H A210003 Alois P. Heinz, <a href="/A210003/b210003.txt">Table of n, a(n) for n = 0..1000</a>
%H A210003 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1,1).
%F A210003 G.f.: -(x^4+1)/(x^5-x^4+2*x-1).
%F A210003 a(n) = 2^n if n<5, and a(n) = 2*a(n-1) -a(n-4) +a(n-5) otherwise.
%e A210003 a(7) = 116 because among the 2^7 = 128 binary words of length 7 only 12, namely 0010001, 0100010, 0100011, 0110001, 1000100, 1000101, 1000110, 1000111, 1010001, 1100010, 1100011 and 1110001 contain the subword 10001.
%p A210003 a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>, <0|0|0|0|1>, <1|-1|0|0|2>>^n. <<1, 2, 4, 8, 16>>)[1, 1]: seq(a(n), n=0..40);
%t A210003 LinearRecurrence[{2,0,0,-1,1},{1,2,4,8,16},40] (* _Harvey P. Dale_, Oct 05 2015 *)
%Y A210003 Columns k=17, 19, 23, 25, 29 of A209972.
%K A210003 nonn,easy
%O A210003 0,2
%A A210003 _Alois P. Heinz_, Mar 16 2012