A331931 The number of regions inside a hexagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

24, 408, 2268, 8208, 20832, 44640, 89214, 154752, 249906, 390012, 590658, 824712, 1183704, 1580868, 2067162, 2770476, 3585582, 4397172, 5665818, 6827736, 8318976, 10209948, 12364098, 14395164, 17194230, 20216808, 23436612, 27124416, 31817676, 35516328

Offset

1,1

Comments

The terms are from numeric computation - no formula for a(n) is currently known.

Links

Table of n, a(n) for n=1..30.

Scott R. Shannon, Hexagon regions for n = 1.

Scott R. Shannon, Hexagon regions for n = 2.

Scott R. Shannon, Hexagon regions for n = 3.

Scott R. Shannon, Hexagon regions for n = 4.

Scott R. Shannon, Hexagon regions for n = 5.

Scott R. Shannon, Hexagon regions for n = 6.

Scott R. Shannon, Hexagon regions for n = 7.

Scott R. Shannon, Hexagon regions for n = 8.

Scott R. Shannon, Hexagon regions for n = 5, with random distance-based coloring.

Scott R. Shannon, Hexagon regions for n = 6, with random distance-based coloring.

Wikipedia, Hexagon.

Crossrefs

Cf. A331932 (n-gons), A330845 (edges), A330846 (vertices), A007678, A092867, A331452, A331929.

Sequence in context: A018206 A021304 A018092 * A227750 A221619 A267166

Adjacent sequences: A331928 A331929 A331930 * A331932 A331933 A331934

Keyword

nonn

Author

Scott R. Shannon and N. J. A. Sloane, Feb 01 2020

Extensions

a(9)-a(30) from Lars Blomberg, May 12 2020

Status

approved