A124723 Number of ternary Lyndon words with exactly five 1's.

2, 12, 56, 224, 806, 2688, 8448, 25344, 73216, 205004, 559104, 1490944, 3899392, 10027008, 25401752, 63504384, 156893184, 383516672, 928514048, 2228433712, 5305794560, 12540968960, 29444014080, 68702699520, 159390262880

Offset: 6

Author

Mike Zabrocki, Nov 05 2006

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A051168, A027376, A124720, A124721, A124722.

Programs

Maple

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

Formula

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.