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

6,1

Links

Table of n, a(n) for n=6..30.

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.

Example

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.

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

Crossrefs

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

Sequence in context: A342319 A127214 A304194 * A122229 A285146 A127216

Adjacent sequences: A124720 A124721 A124722 * A124724 A124725 A124726

Keyword

nonn

Author

Mike Zabrocki, Nov 05 2006

Status

approved