OFFSET
1,2
COMMENTS
Also number of Lyndon words of length n with trace 1 over GF(4).
Let x = RootOf( z^2+z+1 ) and y = 1+x. Also number of Lyndon words of length n with trace x over GF(4). Also number of Lyndon words of length n with trace y over GF(4).
Also number of 4-ary Lyndon words (i.e., Lyndon words over Z_4) of length n with trace 1 (mod 4). Also the same with trace 3 (mod 4). - Andrey Zabolotskiy, Dec 19 2020
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
FORMULA
From Seiichi Manyama, Mar 11 2018: (Start)
a(n) = A000048(2*n) = (1/(4*n)) * Sum_{odd d divides n} mu(d)*4^(n/d), where mu is the Möbius function A008683.
a(n+1) = A300628(n,n) for n >= 0. (End)
From Andrey Zabolotskiy, Dec 19 2020: (Start)
EXAMPLE
a(3; y)=5 since the five Lyndon words over GF(4) of trace y and length 3 are { 00y, 01x, 0x1, 11y, xxy }; the five Lyndon words over Z_4 of trace 1 (mod 4) and length 3 are { 001, 023, 032, 113, 122 }.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 18 2000
EXTENSIONS
More terms from James A. Sellers, Apr 19 2000
STATUS
approved