A124722 Number of ternary Lyndon words with exactly four 1's.

2, 9, 40, 137, 448, 1336, 3840, 10540, 28160, 73168, 186368, 465808, 1146880, 2785024, 6684672, 15875520, 37355520, 87161600, 201850880, 464254208, 1061158912, 2411718656, 5452595200, 12268325888, 27481079808, 61303918592

Offset: 5

Author

Mike Zabrocki, Nov 05 2006

Keywords

• nonn
• easy

Examples

			a(6) = 9 because 111122, 111212, 111123, 111213, 112113, 111132, 111312, 111133, 111313 are all ternary Lyndon words with four 1's
		

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-20,0,76,-96,-32,128,-64).

Crossrefs

Cf. A051168, A027376, A124720, A124721, A124723.

Programs

Mathematica

LinearRecurrence[{8,-20,0,76,-96,-32,128,-64},{2,9,40,137,448,1336,3840,10540},40] (* Harvey P. Dale, Nov 04 2020 *)

Formula

G.f.: x^5*(2-3*x)*(1-x)^2/(1 - 2*x^2)^2/(1 - 2*x)^4 = (1/(1-2*x)^4-1/(1-2*x^2)^2)/4