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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..41.

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.

Sequence in context: A212135 A210569 A334581 * A341877 A005561 A061612

Adjacent sequences:  A341685 A341686 A341687 * A341689 A341690 A341691

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 27 00:02 EDT 2021. Contains 348270 sequences. (Running on oeis4.)