login
A124722
Number of ternary Lyndon words with exactly four 1's.
5
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
5,1
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
EXAMPLE
a(6) = 9 because 111122, 111212, 111123, 111213, 112113, 111132, 111312, 111133, 111313 are all ternary Lyndon words with four 1's
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mike Zabrocki, Nov 05 2006
STATUS
approved