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A124811 Number of 4-ary Lyndon words of length n with exactly three 1s. 4
3, 18, 89, 405, 1701, 6801, 26244, 98415, 360846, 1299078, 4605822, 16120350, 55801305, 191318760, 650483703, 2195382771, 7360989291, 24536630727, 81358302690, 268482398877, 882156452724, 2887057484028, 9414317882700, 30596533116588, 99132767304831 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

Table of n, a(n) for n=4..28.

FORMULA

o.g.f. x^4 (3-9 x+8 x^2)/(1-3x)/(1-3x^3) = 1/3*((x/(1-3*x))^3 - x^3/(1-3*x^3)) a(n) = 1/3*sum_{d|3,d|n} mu(d) C(n/d-1,(n-3)/d )*3^((n-3)/d) = 1/3*C(n-1,2)*3^(n-3) if d=1,2 mod 3 = 1/3*C(n-1,2)*3^(n-3) - 1/3*3^((n-3)/3) if d=0 mod 3

EXAMPLE

a(5) = 18 because 111ab and 11a1b are Lyndon of length 4 for ab=2,3,4.

MATHEMATICA

(3 - 9*x + 8*x^2)/((1 - 3*x)^3*(1 - 3*x^3)) + O[x]^23 // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Sep 19 2017 *)

CROSSREFS

Cf. A124810, A124812, A124813, A124814, A001840, A124721.

Sequence in context: A218924 A037295 A290331 * A006568 A181955 A147518

Adjacent sequences:  A124808 A124809 A124810 * A124812 A124813 A124814

KEYWORD

nonn

AUTHOR

Mike Zabrocki, Nov 08 2006

STATUS

approved

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Last modified June 5 08:21 EDT 2020. Contains 334829 sequences. (Running on oeis4.)