A274586 Number of edges formed by sides and straight "chords" in a right triangle when each side is divided by vertices into n equal segments.

3, 21, 132, 429, 1272, 2826, 5640, 10461, 17094, 26847, 41046, 61041, 84051, 118974, 157209, 204393, 264855, 346524, 428880, 541683, 654087, 793611, 961179, 1167468, 1357515, 1615209, 1891980, 2198019, 2530275, 2957808, 3341439, 3860652, 4371006, 4959636, 5572167, 6277722, 6950064, 7859406, 8763780, 9722571, 10687506, 11934912, 13029834, 14450598, 15805026, 17250795, 18863397, 20763204, 22372839, 24450474

Offset: 1

Author

Cynthia Miaina Rasamimanananivo and Max Alekseyev, Jun 29 2016, Sep 02 2016

Keywords

• nonn

Crossrefs

Cf. A092866, A092867, A274585.

If the boundary points are in general position, we get A367117, A213827, A367118, A367119. - N. J. A. Sloane, Nov 09 2023

Formula

By the Euler characteristic, a(n) = A274585(n) + A092867(n) - 1 = A092866(n) + A092867(n) + 3n - 1.