A369801 - OEIS

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.

1, 3, 6, 10, 15, 19, 24, 27, 32, 35, 40, 43, 48, 51, 56, 59, 64, 67, 72, 75, 80, 83, 88, 91, 96, 99, 104, 107, 112, 115, 120, 123, 128, 131, 136, 139, 144, 147, 152, 155, 160, 163, 168, 171, 176, 179, 184, 187, 192, 195, 200, 203, 208, 211, 216, 219, 224, 227

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Table of n, a(n) for n=2..59.

Bulgarian Winter Mathematical Competition "Atanas Radev", Problems and solutions brochure, Problem 9.4, p. 6 (in Bulgarian).

Art of Problem Solving, High School Olympiads - Colored segments, 2024.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

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.

G.f.: -x^2*(x^7-2*x^4-2*x^3-2*x^2-2*x-1)/((x+1)*(x-1)^2).

a(n) = A047452(n-2) + 2 = A047461(n-1) - 1 for n >= 7. - Hugo Pfoertner, Feb 05 2024