

A344866


Number of polygons formed when every pair of vertices of a regular (2n1)gon are joined by an infinite line.


9



0, 1, 16, 99, 352, 925, 2016, 3871, 6784, 11097, 17200, 25531, 36576, 50869, 68992, 91575, 119296, 152881, 193104, 240787, 296800, 362061, 437536, 524239, 623232, 735625, 862576, 1005291, 1165024, 1343077, 1540800, 1759591, 2000896, 2266209, 2557072, 2875075, 3221856, 3599101, 4008544, 4451967
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OFFSET

1,3


COMMENTS

This is the oddindexed subsequence of A344857. See A344857 for images of the polygons.


LINKS



FORMULA

a(n) = 2*n^4  11*n^3 + 23*n^2  21*n + 7.
G.f.: x^2*(1 + 11*x + 29*x^2 + 7*x^3)/(1  x)^5.  Stefano Spezia, Jun 04 2021


EXAMPLE

a(3) = 16 as the five connected vertices form eleven polygons inside the regular pentagon while also forming five triangles outside the pentagon, giving sixteen polygons in total.


PROG

(Python)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



