%I #22 Jul 02 2014 12:51:39
%S 1,2,4,19,136,3036,151848,16814116,3818273456,1759237059488,
%T 1637673128642016,3074457382841680224,11624286729262765320064,
%U 88424288520685885682129216,1352160640243480723729126645248,41538374868278630828076760060403776,2562126056816477844908944991509312669696
%N For n >= 3, draw a regular n-sided polygon and its n(n-3)/2 diagonals, so there are n(n-1)/2 lines; a(n) is the number of ways to choose a subset of these lines (subsets differing by a rotation or reflection are regarded as identical). a(1)=1, a(2)=2 by convention.
%H Vincenzo Librandi, <a href="/A191563/b191563.txt">Table of n, a(n) for n = 1..80</a>
%H Marc Moskowitz, <a href="http://cnoocy.dreamwidth.org/3312.html">Unique connections of N circularly-spaced points</a>, Feb 05, 2011
%F See Maple program.
%p with(numtheory);
%p f:=proc(n) local t0,t1,d; t0:=0;
%p t1:=divisors(n);
%p for d in t1 do
%p if d mod 2 = 0 then t0:=t0+phi(d)*2^(n^2/(2*d))
%p else t0:=t0+phi(d)*2^(n*(n-1)/(2*d)); fi;
%p od;
%p if n mod 2 = 0 then t0:=t0+n*2^(n^2/4)
%p else t0:=t0+n*2^((n^2-1)/4); fi;
%p t0/(2*n); end;
%p s1:=[seq(f(n),n=1..20)];
%t Table[(2^((n^2-Mod[n,2])/4) + 1/n*(Plus@@ Map[Function[d,EulerPhi[d]*2^((n*(n-Mod[d,2])/2)/d)],Divisors[n]]))/2, {n,1,20}] (* From Olivier GĂ©rard, Aug 27 2011 *)
%Y Suggested by A192314. See A192332 for orbits under cyclic group.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jun 29 2011