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%I #20 Jan 06 2024 12:00:32
%S 3,9,4,48,16,5,237,156,30,6,684,788,460,54,7,1962,2880,2660,888,105,8,
%T 3630,6468,9055,5274,2086,152,9,7617,15800,23000,16914,11830,3400,306,
%U 10,12654,27828,49515,44874,39725,19240,6264,410,11,21114,49936,93995,96630,100569,67632,34947,9170,737,12
%N Table read by antidiagonals: Place k equally spaced points on each side of a regular n-gon and join every pair of these n*k points by a chord; T(n,k) (n >= 3, k >= 0) gives the number of edges in the resulting planar graph.
%C See A367302, A367304, A366485, A367279 for images of the n-gons.
%F a(n,k) = A367302(n,k) + A367304(n,k) - 1 (Euler).
%e The table begins:
%e 3, 9, 48, 237, 684, 1962, 3630, 7617, 12654, 21114, 31170, 50280, 66687, 99342, ...
%e 4, 16, 156, 788, 2880, 6468, 15800, 27828, 49936, 78732, 134656, 173396, ...
%e 5, 30, 460, 2660, 9055, 23000, 49515, 93995, 163100, 264635, 407325, 600550, ...
%e 6, 54, 888, 5274, 16914, 44874, 96630, 182718, 314334, 518832, 804030, 1180314, ...
%e 7, 105, 2086, 11830, 39725, 100569, 213339, 402479, 695240, 1124046, 1726305, ...
%e 8, 152, 3400, 19240, 67632, 169720, 368560, 689408, 1201416, 1935944, 2993104, ...
%e 9, 306, 6264, 34947, 115749, 291132, 614979, 1155708, 1991448, 3214809, ...
%e 10, 410, 9170, 51670, 176460, 440940, 943520, 1764520, 3055110, 4922870, ...
%e 11, 737, 14850, 81620, 268521, 671869, 1415139, 2652837, 4563944, 7358736, ...
%e 12, 780, 17172, 109224, 370584, 924912, 1992528, 3723372, 6442428, 10386180, ...
%e 13, 1534, 30212, 164203, 537303, 1339702, 2815995, 5269758, 9055800, ...
%e 14, 1750, 39774, 217112, 723940, 1795290, 3801168, 7091406, 12223806, ...
%e 15, 2865, 55230, 297600, 969765, 2411595, 5061195, 9459285, 16241160, ...
%e .
%e .
%e .
%Y Cf. A367302 (vertices), A367303 (internal vertices), A367304 (regions), A366485 (first row), A367279 (second row).
%K nonn,tabl
%O 3,1
%A _Scott R. Shannon_, Nov 13 2023