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

Author

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

Keywords

• nonn

Comments

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

Links

• 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.

Extensions

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