OFFSET
0,6
LINKS
Brooke Logan, Table of n, a(n) for n = 0..10000
FORMULA
We argue as in A273724. There are n-1 choices for i.
For nontrivial chords we need i != 5i mod n, which means 4i != 0 mod n, and so when n == 0 mod 4 we must subtract 3 from n-1 and when n == 2 mod 4 we must subtract 1 from n-1.
A chord occurs twice (but must be counted only once) when j==5i mod n and i==5j mod n, thus when 24i == 0 mod n. If n == +/- 3, +/- 9 mod 24 then subtract another 1, if n == +/- 6, +/- 8 mod 24 then subtract another 2, if n==12 mod 24 subtract 4, and if n == 0 mod 24 then subtract another 10.
Putting the pieces together, we obtain the g.f.
x^2/(1-x)^2-(3+x^2)/(1-x^4)-(x^3+x^9+x^15+x^21)/(1-x^24)-2(x^6+x^8+x^16+x^18)/(1-x^24)-(4*x^12+10)/(1-x^24)+13.
The g.f. can also be written as
(14*x^25 - 12*x^24 + 2*x^23 + x^22 + 3*x^21 - 2*x^20 + 2*x^19 + 4*x^17 - x^16 + x^15 + 8*x^13 - 6*x^12 + 2*x^11 + x^10 + 3*x^9 - 2*x^8 + 2*x^7 + 4*x^5 - x^4 + x^3 + 2*x - 2) / ((1-x)*(1-x^24)).
CROSSREFS
KEYWORD
nonn
AUTHOR
Brooke Logan, Jun 25 2016
STATUS
approved