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A374827
Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. The sequence gives the total number of curved edges formed from all circle intersections.
4
1, 2, 9, 28, 150, 636, 3290, 6192, 35145, 57380, 230494, 192588, 1055535, 1177148
OFFSET
1,2
LINKS
Scott R. Shannon, Image for n = 2. In this and other images the starting circles' centers are shown as white dots.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
FORMULA
a(n) = A374825(n) + A374826(n) - 1, by Euler's formula.
CROSSREFS
Cf. A374825 (vertices), A374826 (regions), A374828 (k-gons), A007569 (total circles), A183207, A374339.
Sequence in context: A328281 A324372 A138912 * A002747 A110377 A338436
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Jul 21 2024
STATUS
approved