A340685 The number of regions inside a concave circular triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

1, 12, 28, 102, 187, 462, 868, 1590, 3046, 4398, 6541, 8646, 12256, 15336, 20947, 26610, 33478, 41832, 50821, 64710, 77110, 97878, 113932, 136560, 160849, 185220, 216286, 246450, 289945, 324594, 372976, 426936, 472231, 537366, 598606, 685650, 762736, 858546, 943684, 1043442, 1143751, 1258800

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jan 16 2021

Keywords

• nonn

Comments

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

Links

• Scott R. Shannon, Regions for n = 2.
• Scott R. Shannon, Regions for n = 3.
• Scott R. Shannon, Regions for n = 4.
• Scott R. Shannon, Regions for n = 6.
• Scott R. Shannon, Regions for n = 8.
• Scott R. Shannon, Regions for n = 10.
• Scott R. Shannon, Regions for n = 14.
• Scott R. Shannon, Regions for n = 15.
• Wikipedia, Circular triangle.

Crossrefs

Cf. A340686 (vertices), A340687 (edges), A340688 (n-gons), A340639, A007678, A092867.