A341688 The number of regions inside a 2 by 1 ellipse formed by the straight line segments mutually connecting all points formed by dividing the ellipse into 2n equal angle sectors from its origin.

0, 4, 24, 84, 232, 524, 1052, 1868, 3144, 4876, 7440, 10724, 15124, 20604, 27632, 36124, 46672, 59108, 74184, 91488, 112380, 136044, 163724, 194924, 230932, 271124, 316992, 367748, 425124, 488116, 558820, 635964, 721824, 815044, 918132, 1029524, 1152012, 1283788, 1427964, 1582328, 1750760

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Feb 17 2021

Keywords

• nonn

Comments

The ellipse, with width twice its height, has points at its x-axis extrema and n-1 points both above and below the x-axis, 2n points in total. These are placed on the ellipse's perimeter by dividing it from the origin into 2n sectors of equal angle.

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

Links

• Scott R. Shannon, Regions for n = 3.
• Scott R. Shannon, Regions for n = 5.
• Scott R. Shannon, Regions for n = 9.
• Scott R. Shannon, Regions for n = 19.
• Scott R. Shannon, Regions for n = 24.
• Scott R. Shannon, Regions for n = 13 using random distance-based coloring.
• Wikipedia, Ellipse.

Crossrefs

Cf. A341762 (vertices), A341764 (edges), A341800 (n-gons), A007678, A092867, A255011, A331929, A331931, A333075.