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 A143282 #10 Apr 30 2017 02:59:11
%S A143282 0,0,0,0,1,2,3,5,9,15,24,38,60,94,146,225,345,527,802,1216,1838,2771,
%T A143282 4168,6256,9372,14016,20929,31208,46476,69133,102726,152494,226171,
%U A143282 335169,496320,734440,1086102,1605187,2371049,3500522,5165573,7619251
%N A143282 Number of binary words of length n containing at least one subword 1001 and no subwords 10^{i}1 with i<2.
%H A143282 Alois P. Heinz, <a href="/A143282/b143282.txt">Table of n, a(n) for n = 0..1000</a>
%F A143282 G.f.: x^4/((x^3+x-1)*(x^4+x-1)).
%F A143282 a(n) = A000930(n+2) - A003269(n+4).
%e A143282 a(7) = 5 because 5 binary words of length 7 have at least one subword 1001 and no subwords 11 or 101: 0001001, 0010010, 0100100, 1001000, 1001001.
%p A143282 a:= n-> (Matrix (7, (i, j)-> `if` (i=j-1, 1, `if` (i=7, [-1, 0, -1, 0, 1, -1, 2][j], 0)))^n. <<(0$6), 1>>)[3, 1]: seq (a(n), n=0..50);
%t A143282 CoefficientList[Series[x^4/((x^3+x-1)*(x^4+x-1)), {x,0,50}], x] (* _G. C. Greubel_, Apr 29 2017 *)
%o A143282 (PARI) x='x+O('x^50); concat([0,0,0,0], Vec(x^4/((x^3+x-1)*(x^4+x-1)))) \\ _G. C. Greubel_, Apr 29 2017
%Y A143282 Cf. A000930, A003269, 2nd column of A143291.
%K A143282 nonn
%O A143282 0,6
%A A143282 _Alois P. Heinz_, Aug 04 2008