A359116 -id:A359116 - cp's OEIS frontend

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

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

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.

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

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

A359119 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, in the Farey Ring graph FR(n) defined in A359116.

Original entry on oeis.org

2, 4, 4, 6, 18, 6, 10, 124, 76, 32, 8, 12, 244, 196, 78, 14, 4, 18, 1184, 1296, 534, 118, 28, 2, 22, 2632, 3180, 1244, 330, 58, 2, 28, 7244, 8628, 3594, 962, 190, 38, 32, 12626, 14922, 6378, 1836, 330, 36, 4, 42, 39060, 45656, 20152, 6082, 1252, 132, 28, 2, 46, 56980, 66088, 29454, 8916, 1840, 244, 26, 6

Offset: 2

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

See A359116 and A359117 for further images of the graphs.

			The table begins:
2;
4, 4;
6, 18, 6;
10, 124, 76, 32, 8;
12, 244, 196, 78, 14, 4;
18, 1184, 1296, 534, 118, 28, 2;
22, 2632, 3180, 1244, 330, 58, 2;
28, 7244, 8628, 3594, 962, 190, 38;
32, 12626, 14922, 6378, 1836, 330, 36, 4;
42, 39060, 45656, 20152, 6082, 1252, 132, 28, 2;
46, 56980, 66088, 29454, 8916, 1840, 244, 26, 6;
58, 148058, 170352, 76834, 23936, 4990, 766, 136, 12, 0, 2;
64, 221744, 253808, 115806, 35922, 7428, 1286, 136, 14;
72, 359676, 408252, 188438, 57828, 12432, 1972, 246, 16, 2;
80, 553598, 624588, 291158, 89762, 19066, 3104, 374, 30, 6;
96, 1164192, 1305260, 615048, 189910, 41094, 6654, 844, 72, 12;
102, 1491314, 1664362, 788138, 243924, 52438, 8502, 1080, 112, 2, 2;
120, 2887184, 3203244, 1529870, 474822, 102482, 16490, 2002, 206, 22;
128, 3752194, 4153544, 1987610, 617634, 133288, 21374, 2698, 278, 42;
140, 5393824, 5962776, 2855524, 889822, 191612, 31128, 3926, 438, 26;
.
.

Scott R. Shannon, Image for n = 11.

Cf. A359116 (vertices), A359117 (regions), A359118 (edges), A358889, A006842, A006843, A005728, A331451.

Sum of row n = A359117(n).

A359118 Number of edges in the planar Farey Ring graph FR(n) defined in A359116, including the regions between the convex hull and the bounding circle.

Original entry on oeis.org

1, 2, 12, 48, 457, 1027, 6190, 14652, 40852, 71601, 223637, 325661, 847984, 1269433, 2053303, 3157887, 6638971, 8490949, 16421392, 21323264, 30639928

Offset: 1

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

See A359116 and A359117 for images of the figure.

Cf. A359116 (vertices), A359117 (regions), A359119 (k-gons), A358888, A006842, A006843, A005728, A135565.

a(n) = A359116 + A359117 - 1 by Euler's formula.

cp's OEIS Frontend

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.

Views

Author

Keywords

Links

Crossrefs

Formula

A359119 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, in the Farey Ring graph FR(n) defined in A359116.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A359118 Number of edges in the planar Farey Ring graph FR(n) defined in A359116, including the regions between the convex hull and the bounding circle.

Views

Author

Keywords

Comments

Crossrefs

Formula