%I #4 May 25 2020 23:27:39
%S 3,4,6,7,11,11,14,16,26,22,36,33,40,45,61,50,76,72,81,87,111,95,131,
%T 124,137,146,176,145,201,193,208,218,256,228,286,275,294,307,351,316,
%U 386,374,395,409,461,421,501,486,511,528,586,539,631,615,642,660,726
%N a(n) is the number of vertices in an n-gon formed by the straight line segments connecting vertex k to vertex 2k mod n.
%C See A335057 for illustrations.
%H Lars Blomberg, <a href="/A335059/b335059.txt">Table of n, a(n) for n = 3..270</a>
%F Empirically for n <= 270.
%F Select the row in the table below for which d = n mod m. Then a(n) = (a*n^2+bn+c)/denom.
%F +=============================================+
%F | d | m | a | b | c | denom |
%F +---------------------------------------------+
%F | 1, 5 | 6 | 5 | 0 | 19 | 24 |
%F | 3 | 6 | 5 | -16 | 75 | 24 |
%F | 2, 10 | 12 | 5 | -18 | 64 | 24 |
%F | 4, 8 | 12 | 5 | -18 | 88 | 24 |
%F | 0 | 60 | 5 | -34 | 24 | 24 |
%F | 6, 18, 42, 54 | 60 | 5 | -34 | 192 | 24 |
%F | 12, 24, 36, 48 | 60 | 5 | -34 | 216 | 24 |
%F | 30 | 60 | 5 | -34 | 0 | 24 |
%F +=============================================+
%o (PARI) bc=[[5,0,19,24],[5,-16,75,24],[5,-18,64,24],[5,-18,88,24],[5,-34,24,24],[5,-34,192,24],[5,-34,216,24],[5,-34,0,24]];
%o m=[[1,6,1],[5,6,1],[3,6,2],[2,12,3],[10,12,3],[4,12,4],[8,12,4],[0,60,5],[6,60,6],[18,60,6],[42,60,6],[54,60,6],[12,60,7],[24,60,7],[36,60,7],[48,60,7],[30,60,8]];
%o ix(n)=for(i=1,length(m),x=m[i];if(n%x[2]==x[1], return(x[3])));-1
%o a(n)=x=bc[ix(n)];(x[1]*n^2+x[2]*n+x[3])/x[4]
%o vector(200,x,a(x+2))
%Y Cf. A335057 (regions), A335058 (edges), A335129 (distinct lines).
%K nonn
%O 3,1
%A _Lars Blomberg_, May 24 2020