A290747 Total number of distinct Lyndon factors appearing in all words of length n over an alphabet of size 5.

5, 60, 515, 3800, 25749, 165070, 1018135, 6103350, 35797125, 206363748, 1173148275, 6592732750, 36692520865, 202542849720, 1110149980567, 6047465281420, 32765782091385, 176683116394850, 948690479365355, 5074595254876020, 27051397095965605, 143757461666945890

Offset: 1

Author

N. J. A. Sloane, Aug 11 2017

Keywords

• nonn

Links

• Lars Blomberg, Table of n, a(n) for n = 1..100
• Amy Glen, Jamie Simpson, W. F. Smyth, Counting Lyndon Factors, Electronic Journal of Combinatorics 24(3) (2017), #P3.28.

Programs

PARI

Inner(m,s)=d=divisors(m);sum(i=1,length(d),moebius(m/d[i])*s^d[i]);
Lyndon(s,n) = sum(m=1,n, (n-m+1)/m * s^(n-m) * Inner(m,s));
vector(100,i,Lyndon(5,i)) \\ Lars Blomberg, Aug 12 2017

Extensions

a(11)-a(22) from Lars Blomberg, Aug 12 2017