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A338042
Draw n rays from each of two distinct points in the plane; a(n) is the number of vertices thus created. See Comments for details.
3
2, 2, 4, 2, 8, 4, 14, 8, 22, 14, 32, 22, 44, 32, 58, 44, 74, 58, 92, 74, 112, 92, 134, 112, 158, 134, 184, 158, 212, 184, 242, 212, 274, 242, 308, 274, 344, 308, 382, 344, 422, 382, 464, 422, 508, 464, 554, 508, 602, 554, 652, 602, 704, 652, 758, 704, 814, 758
OFFSET
1,1
COMMENTS
The rays are evenly spaced around each point. The first ray of one point goes opposite to the direction to the other point. Should a ray hit the other point it terminates there, that is, it is converted to a line segment.
See A338041 for illustrations.
FORMULA
a(n) = (n^2 + 7)/4, n odd; (n^2 - 6*n + 16)/4, n even (conjectured).
Conjectured by Stefano Spezia, Oct 08 2020 after Lars Blomberg: (Start)
G.f.: 2*x*(1 - x^2 - x^3 + 2*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: Apparently a(n)=2*(A008795(n-3)+1).
EXAMPLE
For n=1: <-----x x-----> so a(1)=2.
For n=2: <-----x<--->x-----> so a(2)=2.
PROG
(PARI) a(n)=if(n%2==1, (n^2 + 7)/4, (n^2 - 6*n + 16)/4)
vector(200, n, a(n))
CROSSREFS
Cf. A338041 (regions), A338043 (edges), A008795.
Sequence in context: A297112 A259192 A307313 * A131999 A113416 A303140
KEYWORD
nonn
AUTHOR
Lars Blomberg, Oct 08 2020
STATUS
approved