%I #21 Oct 10 2020 03:57:09

%S 2,3,10,7,22,15,38,27,58,43,82,63,110,87,142,115,178,147,218,183,262,

%T 223,310,267,362,315,418,367,478,423,542,483,610,547,682,615,758,687,

%U 838,763,922,843,1010,927,1102,1015,1198,1107,1298,1203,1402,1303,1510,1407

%N Draw n rays from each of two distinct points in the plane; a(n) is the number of edges thus created. See Comments for details.

%C The rays are evenly spaced around each point. The first ray of one point goes in the opposite direction of the other point. Should a ray hit the other point, it terminates there, i.e., it is converted to a line segment.

%C See A338041 for illustrations.

%F a(n) = (n^2 + 4*n - 1)/2, n odd; (n^2 - 2*n + 6)/2, n even (conjectured).

%F Conjectured by _Stefano Spezia_, Oct 08 2020 after _Lars Blomberg_: (Start)

%F G.f.: x*(2 + x + 3*x^2 - 5*x^3 + 3*x^4)/((1 - x)^3*(1 + x)^2).

%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5. (End)

%F _Hugo Pfoertner_, Oct 08 2020: It appears that even terms are 4*A000096+2, odd terms 4*A000124-1.

%e For n=1: <-----x x-----> so a(1)=2.

%e For n=2: <-----x<--->x-----> so a(2)=3.

%o (PARI) a(n)=if(n%2==1,(n^2 + 4*n - 1)/2,(n^2 - 2*n + 6)/2)

%o vector(200, n, a(n))

%Y Cf. A338041 (regions), A338042 (vertices).

%Y Cf. also A000096, A000124.

%K nonn

%O 1,1

%A _Lars Blomberg_, Oct 08 2020