A366484 Place n equally spaced points on each side of an equilateral triangle, and join each of these points by a chord to the 2*n new points on the other two sides: sequence gives number of interior vertices in the resulting planar graph.

0, 0, 13, 96, 285, 901, 1605, 3534, 5797, 9813, 14319, 23809, 30912, 47154, 62728, 82440, 104493, 144730, 173637, 229948, 276325, 336861, 403383, 509146, 582342, 702150, 824875, 969303, 1098225, 1321888, 1463487, 1724094, 1952410, 2221395, 2505064, 2846800, 3103677, 3556029, 3978646, 4443883

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Nov 09 2023

Keywords

• nonn

Comments

See A366483 for further information.

Links

• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 10.

Crossrefs

Cf. A366483 (vertices), A366485 (edges), A366486 (regions).

If the 3*n points are placed "in general position" instead of uniformly, we get sequences A366478, A365929, A366932, A367015.

If the 3*n points are placed uniformly and we also draw chords from the three corner points of the triangle to these 3*n points, we get A274585, A092866, A274586, A092867.

Formula

a(n) = A366485(n) - A366486(n) - 3*n - 2 (Euler).