A278663 Number of periodic necklaces with n beads of 3 colors.

0, 0, 3, 3, 6, 3, 14, 3, 24, 11, 54, 3, 148, 3, 318, 59, 834, 3, 2314, 3, 5952, 323, 16110, 3, 45178, 51, 122646, 2195, 341820, 3, 962634, 3, 2690844, 16115, 7596486, 363, 21568780, 3, 61171662, 122651, 174343026, 3, 498453878, 3, 1426419876, 958819, 4093181694, 3, 11770610128, 315, 33891550302

Offset: 0

Author

Herbert Kociemba, Nov 25 2016

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

Mathematica

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]

Formula

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

a(n) = A001867(n) - A027376(n). - Alois P. Heinz, Nov 25 2016