A344657 Number of vertices formed by infinite lines when connecting all vertices and all points that divide the sides of an equilateral triangle into n equal parts.

3, 10, 85, 310, 999, 2299, 4674, 8878, 14539, 23116, 35922, 53830, 74685, 106957, 140887, 183718, 240108, 315997, 392049, 497518, 599596, 730762, 888903, 1083277, 1257270, 1502830, 1760371, 2047792, 2362620, 2771437, 3129933, 3629443, 4107994, 4670305, 5245447, 5921755

Offset: 1

Author

Scott R. Shannon, Jun 24 2021

Keywords

• nonn

Comments

See A344279 for other images of the polygons.

Links

• Scott R. Shannon, Image of the vertices for n = 3.
• Scott R. Shannon, Image of the vertices for n = 4.

Crossrefs

Cf. A344279 (number of polygons), A344896 (number of edges), A092867 (number polygons inside the triangle), A346446 (number of k-gons), A345649, A146212.

Formula

a(n) = A344896(n) - A344279(n) + 1.