login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124813 Number of 4-ary Lyndon words of length n with exactly five 1s. 4
3, 27, 189, 1134, 6123, 30618, 144342, 649539, 2814669, 11821608, 48361131, 193444524, 758897748, 2927177028, 11123272701, 41712272649, 154580775111, 566796175407, 2058365058057, 7410114208989, 26464693603590, 93829368230910 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

LINKS

Table of n, a(n) for n=6..27.

FORMULA

o.g.f. 3 x^6 (1-6 x+ 18 x^2 - 27 x^3 + 16 x^4)/(1- 3 x)^5/(1- 3 x^5) = 1/5*((x/(1-3*x))^5 - x^5/(1-3*x^5)) a(n) = 1/5*sum_{d|5,d|n} mu(d) C(n/d-1,(n-5)/d )*3^((n-5)/d) = 1/5*C(n-1,4)*3^(n-5) if n=1,2,3,4 mod 5 = 1/5*C(n-1,4)*3^(n-5) - 1/5*3^((n-5)/5) if n=0 mod 5

EXAMPLE

a(7) = 27 because 11111ab, 1111a1b, 111a11b for a,b=2,3,4 are all Lyndon of length 7

MATHEMATICA

3*(1 - 6*x + 18*x^2 - 27*x^3 + 16*x^4)/((1 - 3*x)^5*(1 - 3*x^5)) + O[x]^22 // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Sep 19 2017 *)

CROSSREFS

Cf. A124810, A124811, A124812, A124814, A011795, A124723.

Sequence in context: A241271 A222015 A127215 * A127220 A127222 A248225

Adjacent sequences:  A124810 A124811 A124812 * A124814 A124815 A124816

KEYWORD

nonn

AUTHOR

Mike Zabrocki, Nov 08 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)