A340639 - OEIS

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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.

6

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

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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