A290746 Total number of distinct Lyndon factors appearing in all words of length n over an alphabet of size 2.

2, 9, 30, 87, 234, 597, 1470, 3522, 8264, 19067, 43398, 97659, 217674, 481221, 1056370, 2304676, 5000934, 10799564, 23222114, 49742577, 106181710, 225947089, 479426238, 1014615466, 2142099088, 4512515283, 9486635788, 19906068415, 41696243298, 87196489799

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(2,i)) \\ Lars Blomberg, Aug 12 2017

Extensions

a(11)-a(33) from Lars Blomberg, Aug 12 2017