A340644 The number of vertices on a Reuleaux triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

3, 19, 120, 442, 1332, 2863, 5871, 10171, 17358, 26518, 40590, 57757, 81735, 110209, 148158, 192184, 248772, 313105, 393429, 483283, 593490, 715528, 861660, 1022281, 1211811, 1418515, 1659108, 1919842, 2220204, 2543527, 2912751, 3308305, 3755922, 4233730, 4770150, 5340529, 5977071

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jan 14 2021

Keywords

• nonn

Comments

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

Links

• Scott R. Shannon, Vertices for n = 2.
• Scott R. Shannon, Vertices for n = 3.
• Scott R. Shannon, Vertices for n = 4.
• Scott R. Shannon, Vertices for n = 5.
• Scott R. Shannon, Vertices for n = 6.
• Scott R. Shannon, Vertices for n = 10.
• Scott R. Shannon, Vertices for n = 11.
• Wikipedia, Reuleaux triangle.

Crossrefs

Cf. A340639 (regions), A340613 (edges), A340614 (n-gons), A007678, A092867.