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.

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

Author

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

Keywords

• nonn
• tabf

Comments

See A359116 and A359117 for further images of the graphs.

Examples

			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;
.
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Links

• Scott R. Shannon, Image for n = 11.

Crossrefs

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

Formula

Sum of row n = A359117(n).