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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A331702 for further details. No formula for a(n) is currently known. LINKS Table of n, a(n) for n=1..43. 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 Adjacent sequences: A359043 A359044 A359045 * A359047 A359048 A359049 KEYWORD nonn AUTHOR Scott R. Shannon, Dec 14 2022 STATUS approved

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Last modified August 13 15:21 EDT 2024. Contains 375142 sequences. (Running on oeis4.)