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 A338122 for illustrations.
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..800
FORMULA
a(n) = 2160-a(n-4)+a(n-12)+a(n-16)+a(n-60)+a(n-64)-a(n-72)-a(n-76), n>78. (conjectured)
From Lars Blomberg, Oct 25 2020: (Start)
Conjectured for 3 <= n <= 800.
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 |
+-------------------------------------------+
| 5 | 6 | 3 | 10 | 7 | 4 |
| 1 | 12 | 3 | 10 | 11 | 4 |
| 2, 10 | 12 | 3 | | 28 | 4 |
| 3 | 12 | 3 | 4 | 21 | 4 |
| 6 | 12 | 3 | -10 | 76 | 4 |
| 7 | 12 | 3 | 10 | 35 | 4 |
| 9 | 12 | 3 | 4 | 33 | 4 |
| 4, 20 | 24 | 3 | -12 | 76 | 4 |
| 8, 16 | 24 | 3 | -12 | 124 | 4 |
| 0 | 120 | 3 | -40 | -20 | 4 |
| 12, 36, 84, 108 | 120 | 3 | -40 | 316 | 4 |
| 24, 48, 72, 96 | 120 | 3 | -40 | 364 | 4 |
| 60 | 120 | 3 | -40 | -68 | 4 |
+===========================================+ (End)
EXAMPLE
For n=1 there are three rays that do not intersect, so a(1)=3.
PROG
(PARI)
a(n)=if( \
n%6==5, (3*n^2 + 10*n + 7)/4, \
n%12==1, (3*n^2 + 10*n + 11)/4, \
n%12==2||n%12==10, (3*n^2 + 28)/4, \
n%12==3, (3*n^2 + 4*n + 21)/4, \
n%12==6, (3*n^2 - 10*n + 76)/4, \
n%12==7, (3*n^2 + 10*n + 35)/4, \
n%12==9, (3*n^2 + 4*n + 33)/4, \
n%24==4||n%24==20, (3*n^2 - 12*n + 76)/4, \
n%24==8||n%24==16, (3*n^2 - 12*n + 124)/4, \
n%120==0, (3*n^2 - 40*n - 20)/4, \
n%120==12||n%120==36||n%120==84||n%120==108, (3*n^2 - 40*n + 316)/4, \
n%120==24||n%120==48||n%120==72||n%120==96, (3*n^2 - 40*n + 364)/4, \
n%120==60, (3*n^2 - 40*n - 68)/4, \
-1);
vector(798, n, a(n+2))
CROSSREFS
KEYWORD
nonn
AUTHOR
Lars Blomberg, Oct 11 2020
STATUS
approved