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

1,1

Links

Table of n, a(n) for n=1..50.

Formula

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

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

Sequence in context: A125682 A357783 A360626 * A333030 A125701 A124812

Adjacent sequences: A274583 A274584 A274585 * A274587 A274588 A274589

Keyword

nonn

Author

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

Status

approved