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A359046
Number of distinct regions among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass.
9
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
1,2
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.
FORMULA
a(n) = A359047(n) - A331702(n) + 1 by Euler's formula.
CROSSREFS
Cf. A331702 (vertices), A359047 (edges), A359061 (k-gons), A358782, A007678.
Sequence in context: A019011 A036842 A267844 * A041349 A041016 A351354
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Dec 14 2022
STATUS
approved