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.
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) \\ here R(n) is A289191.
S(n)={sum(i=0, n\2, (-1)^i * sum(j=0, (n-2*i)\2, (2*j)!/j! * if(n%2, if(j, 2*binomial(n\2, i)*binomial(n-2*i-1, 2*j-1)), binomial(n/2, i)*binomial(n-2*i, 2*j) + if(j, binomial(n/2-1, i)*binomial(n-2*i-2, 2*j-2))) / 2))}
R(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}
a(n)={(R(n) + S(n))/2} \\ Andrew Howroyd, Jan 26 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Jun 29 2017
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Jan 26 2020
STATUS
approved