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

1,2

Comments

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

Links

Table of n, a(n) for n=1..42.

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.

Sequence in context: A204386 A078441 A351104 * A203026 A189539 A000546

Adjacent sequences: A340682 A340683 A340684 * A340686 A340687 A340688

Keyword

nonn

Author

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

Status

approved