A274585 Total number of vertices formed by intersections among sides and straight "chords" in a right triangle when each side is divided by vertices into n equal segments.

1, 3, 10, 58, 178, 558, 1255, 2532, 4786, 7804, 12292, 18966, 28540, 39117, 56107, 73924, 96010, 124704, 164815, 203316, 258706, 311296, 377998, 458862, 560827, 649011, 775336, 908974, 1056604, 1215174, 1428283, 1607964, 1866103, 2111587, 2399647, 2694115, 3040309, 3356544, 3811501, 4253191, 4720222, 5180589, 5806813, 6325035, 7036081, 7691035, 8392174, 9180471, 10136431, 10894698, 11930983

Offset: 0

Author

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

Keywords

• nonn

Comments

Total number of points at intersections of sides/"chords" for the triangle in A092866(n).

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 = 6.
• Scott R. Shannon, Image for n = 10.

Crossrefs

Cf. A092866, A092867, A274586.

Formula

a(n) = A092866(n) + 3n.

By the Euler characteristic, a(n) = A274586(n) - A092867(n) + 1.

Extensions

a(0) = 1 added by N. J. A. Sloane, Jan 22 2022