A341762 The number of vertices on 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.

2, 5, 19, 65, 195, 461, 971, 1737, 2995, 4617, 7203, 10385, 14779, 20125, 27155, 35481, 46051, 58277, 73395, 90323, 111403, 134765, 162539, 193385, 229515, 269301, 315331, 365617, 423195, 485617, 556603, 633145, 719299, 811845, 915275, 1025921, 1148811, 1279757, 1424395, 1577723, 1746803

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Feb 19 2021

Keywords

• nonn

Comments

See A341688 for a description of the ellipse.

Curiously the only ellipses found that have vertices with three or more lines crossing that are not on the x or y axes are those with a number of vertices equal to a multiple of ten.

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

Links

• Scott R. Shannon, Image of the vertices for n = 3.
• Scott R. Shannon, Image of the vertices for n = 5. Notice the off-axis vertices that have three lines crossing.
• Scott R. Shannon, Image of the vertices for n = 9.
• Scott R. Shannon, Image of the vertices for n = 10. Notice the off-axis vertices that have three or four lines crossing.
• Scott R. Shannon, Image of the vertices for n = 20. Notice the off-axis vertices that have three or more lines crossing.
• Scott R. Shannon, Image of the vertices for n = 21.
• Wikipedia, Ellipse.

Crossrefs

Cf. A341688 (regions), A341764 (edges), A341800 (n-gons), A007678, A092867, A255011, A331929, A331931, A333075.