A359117 Number of regions in the planar Farey Ring graph FR(n) defined in A359116, including the regions bewteen 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

1,2

Links

Table of n, a(n) for n=1..21.

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.

Formula

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

Crossrefs

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

Sequence in context: A266043 A358962 A265950 * A294264 A367037 A007468

Adjacent sequences: A359114 A359115 A359116 * A359118 A359119 A359120

Keyword

nonn,more

Author

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

Status

approved