A367119 Place n points in general position on each side of an equilateral triangle, and join every pair of the 3*n+3 boundary points by a chord; sequence gives number of edges in the resulting planar graph.

3, 24, 153, 588, 1635, 3708, 7329, 13128, 21843, 34320, 51513, 74484, 104403, 142548, 190305, 249168, 320739, 406728, 508953, 629340, 769923, 932844, 1120353, 1334808, 1578675, 1854528, 2165049, 2513028, 2901363, 3333060, 3811233, 4339104, 4920003, 5557368, 6254745, 7015788

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Nov 05 2023

Keywords

• nonn

Comments

"In general position" implies that the internal lines (or chords) only have simple intersections. There is no interior point where three or more chords meet.

See A367117 and A367118 for images of the triangle.

Crossrefs

Cf. A367117 (vertices), A367118 (regions), A091908, A092098, A331782, A366932.

If the boundary points are equally spaced, we get A274585, A092866, A274586, A092867. - N. J. A. Sloane, Nov 09 2023

Formula

Conjecture: a(n) = (3/2)*(3*n^4 + 4*n^3 + 3*n^2 + 4*n + 2).

a(n) = A367117 (n) + A367118 (n) - 1 by Euler's formula.