A359119 - OEIS

%I #12 Dec 17 2022 23:36:59

%S 2,4,4,6,18,6,10,124,76,32,8,12,244,196,78,14,4,18,1184,1296,534,118,

%T 28,2,22,2632,3180,1244,330,58,2,28,7244,8628,3594,962,190,38,32,

%U 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

%N 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.

%C See A359116 and A359117 for further images of the graphs.

%H Scott R. Shannon, <a href="/A359119/a359119.jpg">Image for n = 11</a>.

%F Sum of row n = A359117(n).

%e The table begins:

%e 2;

%e 4, 4;

%e 6, 18, 6;

%e 10, 124, 76, 32, 8;

%e 12, 244, 196, 78, 14, 4;

%e 18, 1184, 1296, 534, 118, 28, 2;

%e 22, 2632, 3180, 1244, 330, 58, 2;

%e 28, 7244, 8628, 3594, 962, 190, 38;

%e 32, 12626, 14922, 6378, 1836, 330, 36, 4;

%e 42, 39060, 45656, 20152, 6082, 1252, 132, 28, 2;

%e 46, 56980, 66088, 29454, 8916, 1840, 244, 26, 6;

%e 58, 148058, 170352, 76834, 23936, 4990, 766, 136, 12, 0, 2;

%e 64, 221744, 253808, 115806, 35922, 7428, 1286, 136, 14;

%e 72, 359676, 408252, 188438, 57828, 12432, 1972, 246, 16, 2;

%e 80, 553598, 624588, 291158, 89762, 19066, 3104, 374, 30, 6;

%e 96, 1164192, 1305260, 615048, 189910, 41094, 6654, 844, 72, 12;

%e 102, 1491314, 1664362, 788138, 243924, 52438, 8502, 1080, 112, 2, 2;

%e 120, 2887184, 3203244, 1529870, 474822, 102482, 16490, 2002, 206, 22;

%e 128, 3752194, 4153544, 1987610, 617634, 133288, 21374, 2698, 278, 42;

%e 140, 5393824, 5962776, 2855524, 889822, 191612, 31128, 3926, 438, 26;

%e .

%e .

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

%K nonn,tabf

%O 2,1

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