A191563 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.

1, 2, 4, 19, 136, 3036, 151848, 16814116, 3818273456, 1759237059488, 1637673128642016, 3074457382841680224, 11624286729262765320064, 88424288520685885682129216, 1352160640243480723729126645248, 41538374868278630828076760060403776, 2562126056816477844908944991509312669696

Offset: 1

Author

N. J. A. Sloane, Jun 29 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..80
• Marc Moskowitz, Unique connections of N circularly-spaced points, Feb 05, 2011

Crossrefs

Suggested by A192314. See A192332 for orbits under cyclic group.

Programs

Maple

with(numtheory);
f:=proc(n) local t0,t1,d; t0:=0;
t1:=divisors(n);
for d in t1 do
if d mod 2 = 0 then t0:=t0+phi(d)*2^(n^2/(2*d))
else t0:=t0+phi(d)*2^(n*(n-1)/(2*d)); fi;
od;
if n mod 2 = 0 then t0:=t0+n*2^(n^2/4)
else t0:=t0+n*2^((n^2-1)/4); fi;
t0/(2*n); end;
s1:=[seq(f(n),n=1..20)];

Mathematica

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 Gérard, Aug 27 2011 *)

Formula

See Maple program.