OFFSET
1,2
COMMENTS
The case n=2 is a degenerate polygon (two sides connecting two vertices). The two possibilities are when the edges cross and do not cross. Polygons start at n=3 with a triangle.
The sequence A132102 enumerates the case that edges are allowed between exits on the same side. This sequence can be enumerated in a similar manner using inclusion-exclusion on the number of sides that have their two exits connected. - Andrew Howroyd, Jan 26 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Marko Riedel, Hexagonal tiles.
Marko Riedel, Maple code to compute number of tiles by ordinary enumeration and by Power Group Enumeration.
Marko Riedel, Maple code for number of tiles using Burnside lemma.
PROG
(PARI) a(n) = {sumdiv(n, d, my(m=n/d); eulerphi(d)*sum(i=0, m, (-1)^i * binomial(m, i) * sum(j=0, m-i, (d%2==0 || m-i-j==0) * binomial(2*(m-i), 2*j) * d^j * (2*j)! / (j!*2^j) )))/n} \\ Andrew Howroyd, Jan 26 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Jun 27 2017
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Jan 26 2020
STATUS
approved