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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.

%I A338042 #23 Oct 19 2020 16:41:48
%S A338042 2,2,4,2,8,4,14,8,22,14,32,22,44,32,58,44,74,58,92,74,112,92,134,112,
%T A338042 158,134,184,158,212,184,242,212,274,242,308,274,344,308,382,344,422,
%U A338042 382,464,422,508,464,554,508,602,554,652,602,704,652,758,704,814,758
%N 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.
%C A338042 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.
%C A338042 See A338041 for illustrations.
%F A338042 a(n) = (n^2 + 7)/4, n odd; (n^2 - 6*n + 16)/4, n even (conjectured).
%F A338042 Conjectured by _Stefano Spezia_, Oct 08 2020 after _Lars Blomberg_: (Start)
%F A338042 G.f.: 2*x*(1 - x^2 - x^3 + 2*x^4)/((1 - x)^3*(1 + x)^2).
%F A338042 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5. (End)
%F A338042 _Hugo Pfoertner_, Oct 08 2020: Apparently a(n)=2*(A008795(n-3)+1).
%e A338042 For n=1:    <-----x     x----->   so a(1)=2.
%e A338042 For n=2:    <-----x<--->x----->   so a(2)=2.
%o A338042 (PARI) a(n)=if(n%2==1,(n^2 + 7)/4,(n^2 - 6*n + 16)/4)
%o A338042 vector(200, n, a(n))
%Y A338042 Cf. A338041 (regions), A338043 (edges), A008795.
%K A338042 nonn
%O A338042 1,1
%A A338042 _Lars Blomberg_, Oct 08 2020