A329713 The number of regions inside a heptagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

50, 868, 5594, 18396, 48462, 101794, 195714, 336504, 549704, 841890, 1249676, 1774612, 2468572, 3328234, 4414054, 5725034, 7336855, 9233098, 11513419, 14149296, 17254434, 20805554, 24928380, 29573348, 34902155, 40861422, 47613161

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

Crossrefs

Cf. A329714 (n-gons), A333112 (edges), A333113 (vertices), A007678, A092867, A331452, A331931.

Extensions

a(8)-a(27) from Lars Blomberg, May 13 2020