A338043 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.

2, 3, 10, 7, 22, 15, 38, 27, 58, 43, 82, 63, 110, 87, 142, 115, 178, 147, 218, 183, 262, 223, 310, 267, 362, 315, 418, 367, 478, 423, 542, 483, 610, 547, 682, 615, 758, 687, 838, 763, 922, 843, 1010, 927, 1102, 1015, 1198, 1107, 1298, 1203, 1402, 1303, 1510, 1407

Offset: 1

Author

Lars Blomberg, Oct 08 2020

Keywords

• nonn

Comments

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.

See A338041 for illustrations.

Examples

			For n=1:    <-----x     x----->   so a(1)=2.
For n=2:    <-----x<--->x----->   so a(2)=3.
		

Crossrefs

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

Cf. also A000096, A000124.

Programs

PARI

a(n)=if(n%2==1,(n^2 + 4*n - 1)/2,(n^2 - 2*n + 6)/2)
vector(200, n, a(n))

Formula

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

Conjectured by Stefano Spezia, Oct 08 2020 after Lars Blomberg: (Start)

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

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

Hugo Pfoertner, Oct 08 2020: It appears that even terms are 4*A000096+2, odd terms 4*A000124-1.