A359117 Number of regions in the planar Farey Ring graph FR(n) defined in A359116, including the regions between the convex hull and the bounding circle.

1, 2, 8, 30, 250, 548, 3180, 7468, 20684, 36164, 112406, 163600, 425144, 636208, 1028934, 1581766, 3323182, 4249976, 8216442, 10668790, 15329216

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Dec 17 2022

Keywords

• nonn
• more

Links

• 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.

Crossrefs

Cf. A359116 (vertices), A359118 (edges), A359119 (k-gons), A358886, A006842, A006843, A005728, A007678.

Formula

a(n) = A359118 - A359116 + 1 by Euler's formula.