OFFSET
0,6
COMMENTS
The number of length 2n balanced binary Lyndon words is A022553(n) and the number which are equivalent to their reverse, complement and reversed complement are respectively A045680(n), A000048(n) and A000740(n). - Andrew Howroyd, Sep 29 2017
LINKS
Jean-François Alcover, Table of n, a(n) for n = 0..100
FORMULA
MATHEMATICA
a22553[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d]*Binomial[2d, d], {d, Divisors[n]}]/(2n)];
a45680[n_] := If[n == 0, 1, DivisorSum[n, MoebiusMu[n/#] Binomial[# - Mod[#, 2], Quotient[#, 2]] &]];
a48[n_] := If[n == 0, 1, Total[MoebiusMu[#]*2^(n/#)& /@ Select[Divisors[n], OddQ]]/(2n)];
a740[n_] := Sum[MoebiusMu[n/d]*2^(d - 1), {d, Divisors[n]}];
b[n_] := Module[{t = 0, r = n}, If[n == 0, 1, While[EvenQ[r], r = Quotient[r, 2]; t += 2^(r - 1)]]; t + 2^Quotient[r, 2]];
a45683[n_] := If[n == 0, 1, DivisorSum[n, MoebiusMu[n/#]*b[#] &]];
a[n_] := If[n == 0, 0, a22553[n] - a45680[n] - a48[n] - a740[n] + 2 a45683[n]];
a /@ Range[0, 100] (* Jean-François Alcover, Sep 23 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved