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 A124723 #9 Jan 23 2015 10:57:29 %S A124723 2,12,56,224,806,2688,8448,25344,73216,205004,559104,1490944,3899392, %T A124723 10027008,25401752,63504384,156893184,383516672,928514048,2228433712, %U A124723 5305794560,12540968960,29444014080,68702699520,159390262880 %N A124723 Number of ternary Lyndon words with exactly five 1's. %F A124723 G.f.: 2*x^6*(1-2*x+3*x^2)*(1-x)^2/(1-2*x^5)/(1-2*x)^5= (1/(1-2*x)^5-1/(1-2*x^5))/5. %e A124723 a(7) = 12 because 11111ab, 1111a1b, 111a11b where ab = 22, 23, 32 or 33 are all ternary Lyndon words of length 7 with five 1's. %p A124723 a:= n-> (Matrix([[806, 224, 56, 12, 2, 0$5]]). Matrix(10, (i,j)-> `if`(i=j-1, 1, `if`(j=1, [10, -40, 80, -80, 34, -20, 80, -160, 160, -64] [i], 0)))^(n-10))[1,1]: seq(a(n), n=6..30); # _Alois P. Heinz_, Aug 04 2008 %Y A124723 Cf. A051168, A027376, A124720, A124721, A124722. %K A124723 nonn %O A124723 6,1 %A A124723 _Mike Zabrocki_, Nov 05 2006