A340639 The number of regions inside a Reuleaux triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

1, 24, 145, 516, 1432, 3084, 6106, 10638, 17764, 27336, 41233, 58902, 82675, 111864, 149497, 194430, 250534, 316020, 395728, 487122, 596434, 720162, 865321, 1027974, 1216291, 1425348, 1664539, 1928022, 2226658, 2553204, 2920378, 3319536, 3764848, 4246638, 4780489, 5355414, 5988973

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..37.

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 = 5.

Scott R. Shannon, Regions for n = 6.

Scott R. Shannon, Regions for n = 10.

Scott R. Shannon, Regions for n = 11.

Scott R. Shannon, Regions for n = 9 with random distance-based coloring.

Scott R. Shannon, Regions for n = 10 with random distance-based coloring.

Wikipedia, Reuleaux triangle.

Crossrefs

Cf. A340644 (vertices), A340613 (edges), A340614 (n-gons), A007678, A092867.

Sequence in context: A158047 A042116 A215756 * A290313 A042118 A039494

Adjacent sequences: A340636 A340637 A340638 * A340640 A340641 A340642

Keyword

nonn

Author

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

Status

approved