A054664 - OEIS

%I #18 Dec 19 2020 18:44:50

%S 1,1,5,14,51,165,585,2032,7280,26163,95325,349350,1290555,4792905,

%T 17895679,67106816,252645135,954429840,3616814565,13743869130,

%U 52357696365,199911109725,764877654105,2932030657200,11258999068416

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

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

%H F. Ruskey, <a href="http://combos.org/TSlyndon">Number of q-ary Lyndon words with given trace mod q</a>

%F From _Andrey Zabolotskiy_, Dec 19 2020: (Start)

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

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

%t a[n_] := 1/(4 n) Sum[GCD[d, 4] MoebiusMu[d] 4^(n/d), {d, Divisors[n]}];

%t Array[a, 30] (* _Andrey Zabolotskiy_, Dec 19 2020 *)

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

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Apr 18 2000

%E More terms from _James A. Sellers_, Apr 19 2000