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 A358782 The number of regions formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter. 16
 1, 7, 12, 66, 85, 281, 264, 802, 821, 1893, 1740, 3810, 3725, 6871, 6448, 11748, 11125, 18317, 17160, 27616, 26797, 40067, 37176, 56826, 54653, 77707, 74788, 103734, 101041, 136835, 131744, 176584, 172109, 223931, 216900, 281090, 273829, 348583, 337480, 425950, 416641 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Conjecture: for odd values of n all vertices are simple, other than those defining the diameters of the circles. No formula for n, or only the odd values of n, is currently known. The author thanks Zach Shannon some of whose code was used in the generation of this sequence. If n is odd, the circle containing the initial n points is not part of the graph (compare A370976-A370979). - N. J. A. Sloane, Mar 25 2024 LINKS Table of n, a(n) for n=2..42. Scott R. Shannon, Image for n = 2. In this and other images the points defining the circle diameters 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 = 17. Scott R. Shannon, Image for n = 20. Scott R. Shannon, Image for n = 23. FORMULA a(n) = A358783(n) - A358746(n) + 1 by Euler's formula. CROSSREFS Cf. A358746 (vertices), A358783 (edges), A359009 (k-gons), A007678, A344857. See allso A370976-A370979. Sequence in context: A266056 A083335 A372734 * A119179 A121983 A177169 Adjacent sequences: A358779 A358780 A358781 * A358783 A358784 A358785 KEYWORD nonn AUTHOR Scott R. Shannon, Nov 30 2022 STATUS approved

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Last modified August 10 13:32 EDT 2024. Contains 375056 sequences. (Running on oeis4.)