A054664 Number of 4-ary Lyndon words of length n with trace 0 mod 4.

1, 1, 5, 14, 51, 165, 585, 2032, 7280, 26163, 95325, 349350, 1290555, 4792905, 17895679, 67106816, 252645135, 954429840, 3616814565, 13743869130, 52357696365, 199911109725, 764877654105, 2932030657200, 11258999068416

Offset

1,3

Comments

Also number of 4-ary Lyndon words of length n with trace 2 mod 4.

Links

Table of n, a(n) for n=1..25.

F. Ruskey, Number of q-ary Lyndon words with given trace mod q

Formula

From Andrey Zabolotskiy, Dec 19 2020: (Start)

a(n) = A068596(n) + A074403(n) + A074404(n) + A074405(n).

a(n) = A074410(n) + A074411(n) + A074412(n) + A074413(n). (End)

Mathematica

a[n_] := 1/(4 n) Sum[GCD[d, 4] MoebiusMu[d] 4^(n/d), {d, Divisors[n]}];
Array[a, 30] (* Andrey Zabolotskiy, Dec 19 2020 *)

Crossrefs

Cf. A000048, A051841, A046211, A046209, A054660, etc.

Sequence in context: A107242 A203164 A063835 * A091218 A197601 A133751

Adjacent sequences: A054661 A054662 A054663 * A054665 A054666 A054667

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 18 2000

Extensions

More terms from James A. Sellers, Apr 19 2000

Status

approved