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

1,1

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

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

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.

Sequence in context: A047116 A148433 A148434 * A341878 A062122 A148435

Adjacent sequences:  A341758 A341759 A341761 * A341763 A341764 A341765

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)