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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
1, 8, 30, 120, 618, 3536, 22668, 151848, 1054986, 7472984, 53737896, 390582648, 2863716060, 21145502960, 157076310324, 1172820793824, 8796118712586, 66229473393728, 500400163666188, 3792505486235544, 28823039252629512, 219604100410657136, 1676976747053723292 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 11:24 EDT 2022. Contains 357070 sequences. (Running on oeis4.)