A359117 - OEIS

%I #12 Dec 17 2022 23:27:22

%S 1,2,8,30,250,548,3180,7468,20684,36164,112406,163600,425144,636208,

%T 1028934,1581766,3323182,4249976,8216442,10668790,15329216

%N 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.

%H Scott R. Shannon, <a href="/A359117/a359117.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_1.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_2.jpg">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_3.jpg">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_4.jpg">Image for n = 7</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_5.jpg">Image for n = 8</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_6.jpg">Image for n = 9</a>.

%H Scott R. Shannon, <a href="/A359117/a359117_7.jpg">Image for n = 10</a>.

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

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

%K nonn,more

%O 1,2

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 17 2022