A333075 The number of regions inside an octagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

80, 1488, 9312, 31552, 83432, 174816, 339816, 584176, 953416, 1463936, 2173976, 3074784, 4294080, 5790816, 7664880, 9952944, 12757088, 16036096, 20013696, 24577760, 29973528, 36161472, 43314312, 51334672

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Mar 07 2020

Keywords

• nonn
• more

Comments

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

Links

• Scott R. Shannon, Octagon regions for n = 1.
• Scott R. Shannon, Octagon regions for n = 2.
• Scott R. Shannon, Octagon regions for n = 3.
• Scott R. Shannon, Octagon regions for n = 4.
• Scott R. Shannon, Octagon regions using random distance-based coloring for n = 2.
• Scott R. Shannon, Octagon regions using random distance-based coloring for n = 3.
• Scott R. Shannon, Octagon regions using random distance-based coloring for n = 4.
• Wikipedia, Octagon.

Crossrefs

Cf. A333076 (n-gons), A333109 (vertices), A333110 (edges), A007678, A092867, A331452, A331931.

Extensions

a(7)-a(24) from Lars Blomberg, May 14 2020