A344657 - OEIS

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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.

6

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

(list; graph; refs; listen; history; text; internal format)

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