|
|
A032167
|
|
Number of aperiodic necklaces of n beads of 12 colors.
|
|
3
|
|
|
12, 66, 572, 5148, 49764, 497354, 5118828, 53745120, 573308736, 6191711526, 67546215516, 743008120140, 8230246567620, 91708459194066, 1027134771622388, 11555266154065920, 130506535690613940
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
"CHK" (necklace, identity, unlabeled) transform of 12, 0, 0, 0...
a(n) = Sum_{d|n} mu(d)*12^(n/d)/n.
G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 12*x^k))/k. - Ilya Gutkovskiy, May 19 2019
|
|
MATHEMATICA
|
f[d_]:=MoebiusMu[d] 12^(n/d)/n; a[n_]:=Total[f/@Divisors[n]]; a[0]=1; Table[a[n], {n, 1, 30}] (* Vincenzo Librandi, Oct 14 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|