A359046 Number of distinct regions among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass.

1, 3, 7, 45, 66, 186, 267, 657, 721, 1501, 1893, 2772, 3654, 5727, 6511, 9969, 11340, 14850, 18051, 23921, 26755, 35201, 39975, 47280, 55776, 69863, 75385, 93017, 102864, 117810, 134541, 161217, 172921, 205293, 221271, 252828, 277242, 322811, 341017, 393721, 420702, 466074, 509379

Offset: 1

Author

Scott R. Shannon, Dec 14 2022

Keywords

• nonn

Comments

See A331702 for further details.

No formula for a(n) is currently known.

Links

• Scott R. Shannon, Image for n = 2. In this and other images the points defining the n-sided regular polygon are show as white dots.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 6.
• Scott R. Shannon, Image for n = 7.
• Scott R. Shannon, Image for n = 8.
• Scott R. Shannon, Image for n = 9.
• Scott R. Shannon, Image for n = 10.
• Scott R. Shannon, Image for n = 11.
• Scott R. Shannon, Image for n = 12.
• Scott R. Shannon, Image for n = 18.
• Scott R. Shannon, Image for n = 21.
• Scott R. Shannon, Image for n = 25.

Crossrefs

Cf. A331702 (vertices), A359047 (edges), A359061 (k-gons), A358782, A007678.

Formula

a(n) = A359047(n) - A331702(n) + 1 by Euler's formula.