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

0,2

Comments

If the group is changed to C_n we get A054627.

Links

Table of n, a(n) for n=0..22.

Formula

For formula see Maple code.

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

Crossrefs

Cf. A161221, A054627.

Sequence in context: A239612 A055737 A293965 * A229374 A215471 A221145

Adjacent sequences: A161219 A161220 A161221 * A161223 A161224 A161225

Keyword

nonn

Author

H. O. Pollak (hpollak(AT)adsight.com) and N. J. A. Sloane, Nov 21 2009

Status

approved