A344279 Number of polygons formed by infinite lines when connecting all vertices and all points that divide the sides of an equilateral triangle into n equal parts.

1, 12, 102, 396, 1198, 2748, 5539, 10272, 16986, 26934, 41179, 60804, 84769, 119022, 157947, 206352, 268030, 347430, 432820, 543210, 659238, 801804, 970429, 1171662, 1371040, 1627398, 1904550, 2213712, 2555320, 2971260, 3373399, 3881838, 4399329, 4988502, 5610543, 6315312

Offset

1,2

Links

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

Scott R. Shannon, Image for n = 2. In this and other images the triangle's points are highlighted as white dots while the outer open regions, which are not counted, are darkened. The key for the edge-number coloring is shown at the top-left of the image.

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 = 7.

Scott R. Shannon, Image for n = 8.

Formula

a(n) = A344896(n) - A344657(n) + 1.

Crossrefs

Cf. A344657 (number of vertices), A344896 (number of edges), A346446 (number of k-gons), A092867 (number polygons inside the triangle), A343755 (number of regions), A345459, A344857.

Sequence in context: A099299 A344366 A304504 * A022736 A261483 A082151

Adjacent sequences: A344276 A344277 A344278 * A344280 A344281 A344282

Keyword

nonn

Author

Scott R. Shannon, Jun 22 2021

Status

approved