cp's OEIS Frontend

A369801 Maximum number of segments between n points on a circle so that they can be colored in 2 colors so that each of them intersects (at an internal point) at most one other segment of the same color.

%I A369801 #34 Mar 30 2024 02:39:53
%S A369801 1,3,6,10,15,19,24,27,32,35,40,43,48,51,56,59,64,67,72,75,80,83,88,91,
%T A369801 96,99,104,107,112,115,120,123,128,131,136,139,144,147,152,155,160,
%U A369801 163,168,171,176,179,184,187,192,195,200,203,208,211,216,219,224,227
%N A369801 Maximum number of segments between n points on a circle so that they can be colored in 2 colors so that each of them intersects (at an internal point) at most one other segment of the same color.
%H A369801 Bulgarian Winter Mathematical Competition "Atanas Radev", <a href="https://mgyambol.com/docs/Broshura_ZMS_2024.pdf">Problems and solutions brochure</a>, Problem 9.4, p. 6 (in Bulgarian).
%H A369801 Art of Problem Solving, <a href="https://artofproblemsolving.com/community/c6h3244051p29752645">High School Olympiads - Colored segments</a>, 2024.
%H A369801 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A369801 a(n) = n*(n-1)/2 for n<=6, a(2*k+1) = 8*k-5 if k>=3, a(2*k) = 8*k-8 if k>=4.
%F A369801 G.f.: -x^2*(x^7-2*x^4-2*x^3-2*x^2-2*x-1)/((x+1)*(x-1)^2).
%F A369801 a(n) = A047452(n-2) + 2 = A047461(n-1) - 1 for n >= 7. - _Hugo Pfoertner_, Feb 05 2024
%t A369801 Drop[CoefficientList[Series[ -x^2*(x^7-2*x^4-2*x^3-2*x^2-2*x-1)/((x+1)*(x-1)^2),{x,0,59}],x],2] (* _James C. McMahon_, Mar 08 2024 *)
%o A369801 (Python)
%o A369801 def A369801(n): return (n-2<<2)-(n&1) if n>=7 else (1, 3, 6, 10, 15)[n-2] # _Chai Wah Wu_, Mar 30 2024
%Y A369801 Cf. A047452, A047461.
%K A369801 nonn,easy
%O A369801 2,2
%A A369801 _Mladen Valkov_, Feb 01 2024