A161222 Consider necklaces with n beads, each of one of four colors (say C1, C2, C3, C4), where the n segments of cord between the beads are each colored red or green; a(n) is the number of different necklaces under the action of the dihedral group D_{2n}.
1, 8, 30, 120, 618, 3536, 22668, 151848, 1054986, 7472984, 53737896, 390582648, 2863716060, 21145502960, 157076310324, 1172820793824, 8796118712586, 66229473393728, 500400163666188, 3792505486235544, 28823039252629512, 219604100410657136, 1676976747053723292
Offset: 0
Keywords
Programs
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Maple
with(numtheory); f:=proc(n) local t1,d,m; if n mod 2 = 0 then m:=n/2; t1:=3*2^(3*m); else m:=(n-1)/2; t1:=2^(3*m+3); fi; (1/2)*( (1/n) * add( phi(d)*2^(3*n/d), d in divisors(n)) + t1 ); end; # this assumes n>0
Formula
For formula see Maple code.
Comments