OFFSET
1,1
COMMENTS
The rays are evenly spaced around each point. The first ray from each point goes opposite to the direction to the center of the circle. Should a ray hit another point it is terminated there.
See A338421 for illustrations.
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..642
FORMULA
Conjectured for 3 <= n <= 642.
Select the row in the table below for which r = n mod m. Then a(n)=(a*n^2 + b*n + c)/d.
+==================================+
| r | m | a | b | c | d |
+----------------------------------+
| 2 | 4 | 3 | -6 | 18 | 2 |
| 3 | 4 | 3 | 6 | 3 | 2 |
| 1 | 8 | 3 | 6 | 7 | 2 |
| 4 | 8 | 3 | -10 | 34 | 2 |
| 5 | 8 | 3 | 6 | 23 | 2 |
| 0 | 48 | 3 | -39 | -110 | 2 |
| 8, 40 | 48 | 3 | -39 | 194 | 2 |
| 16, 32 | 48 | 3 | -39 | 226 | 2 |
| 24 | 48 | 3 | -39 | 114 | 2 |
+==================================+
EXAMPLE
For n=1 there are four rays that do not intersect, so a(1)=4.
PROG
(PARI)
a(n)={ if(
n==1, 4,
n==2, 5,
n%4==2, (3*n^2 - 6*n + 18)/2,
n%4==3, (3*n^2 + 6*n + 3)/2,
n%8==1, (3*n^2 + 6*n + 7)/2,
n%8==4, (3*n^2 - 10*n + 34)/2,
n%8==5, (3*n^2 + 6*n + 23)/2,
n%48==0, (3*n^2 - 39*n - 110)/2,
n%48==8||n%48==40, (3*n^2 - 39*n + 194)/2,
n%48==16||n%48==32, (3*n^2 - 39*n + 226)/2,
n%48==24, (3*n^2 - 39*n + 114)/2,
-1); }
vector(642, n, a(n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Lars Blomberg, Oct 26 2020
STATUS
approved