A278663 - OEIS

%I #8 Nov 25 2016 20:18:48

%S 0,0,3,3,6,3,14,3,24,11,54,3,148,3,318,59,834,3,2314,3,5952,323,16110,

%T 3,45178,51,122646,2195,341820,3,962634,3,2690844,16115,7596486,363,

%U 21568780,3,61171662,122651,174343026,3,498453878,3,1426419876,958819,4093181694,3,11770610128,315,33891550302

%N Number of periodic necklaces with n beads of 3 colors.

%F G.f.: k=3, Sum_{i>=1} (mu(i) - phi(i))*log(1 - k*x^i)/i.

%F a(n) = A001867(n) - A027376(n). - _Alois P. Heinz_, Nov 25 2016

%e Example: The 6 periodic necklaces with 4 beads and the colors A, B and C are AAAA, BBBB, CCCC, ABAB, ACAC and BCBC.

%t mx=40;f[x_,k_]:=Sum[(MoebiusMu[i]-EulerPhi[i])Log[1-k*x^i]/i,{i,1,mx}];CoefficientList[Series[f[x,3],{x,0,mx}],x]

%Y Cf. A001867, A027376, A066656 (2 colors).

%K nonn

%O 0,3

%A _Herbert Kociemba_, Nov 25 2016