A344311 Number of polygons formed outside a regular n-gon when every pair of vertices of the n-gon are joined by an infinite line.

0, 0, 0, 0, 5, 18, 49, 96, 198, 320, 550, 708, 1235, 1582, 2415, 2912, 4284, 4518, 7068, 8080, 11025, 12430, 16445, 16992, 23650, 26000, 32994, 35896, 44863, 42090, 59675, 64064, 77880, 83232, 99960, 102132, 126429, 133950, 157833, 166560, 194750, 191310, 237790, 249480, 287595, 301070

Offset

1,5

Comments

See A344857 for other examples and images of the polygons.

Only finite polygons are counted. - N. J. A. Sloane, Jun 11 2021

Links

Table of n, a(n) for n=1..46.

Formula

For odd n, a(n) = (2*n^4 - 15*n^3 + 34*n^2 - 21*n)/24 (see A344857).

a(n) = A344857(n) - A007678(n).

Example

a(5) = 5 as the five connected vertices of a regular pentagon form five triangles outside the pentagon, along with sixteen polygons on the inside.

Crossrefs

Cf. A344857 (total number of polygons), A007678 (number of polygons inside the n-gon), A345025 (total number of polygons and open regions), A344938, A344857, A344866, A146213 (number of vertices).

Sequence in context: A109363 A218214 A146213 * A176145 A270978 A272512

Adjacent sequences: A344308 A344309 A344310 * A344312 A344313 A344314

Keyword

nonn

Author

Scott R. Shannon, Jun 01 2021

Extensions

Edited by N. J. A. Sloane, Sep 12 2021

Status

approved