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

1,1

Comments

See A344279 for other images of the polygons.

Links

Table of n, a(n) for n=1..36.

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

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

Formula

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

Crossrefs

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

Sequence in context: A341848 A136505 A006311 * A224774 A034792 A135457

Adjacent sequences: A344654 A344655 A344656 * A344658 A344659 A344660

Keyword

nonn

Author

Scott R. Shannon, Jun 24 2021

Status

approved