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%I #15 Jan 05 2024 12:50:13
%S 3,3,4,3,8,5,3,8,20,6,3,8,35,42,7,3,8,50,66,91,8,3,8,65,66,308,136,9,
%T 3,8,80,66,630,232,288,10,3,8,95,66,1057,232,1305,390,11,3,8,110,66,
%U 1589,232,2808,900,715,12,3,8,125,66,2226,232,4581,1050,3399,756,13
%N Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of edges in a regular n-gon after k generations of mitosis.
%C See A350000 for further details and images of the n-gons.
%e The table begins:
%e .
%e | Number of edges after k generations
%e n\k | 0, 1, 2, 3, 4, 5, 6, 7, 8, ...
%e ----------------------------------------------------------------------------------
%e 3 | 3, 3, 3, 3, 3, 3, 3, 3, 3, ...
%e 4 | 4, 8, 8, 8, 8, 8, 8, 8, 8, ...
%e 5 | 5, 20, 35, 50, 65, 80, 95, 110, 125, ...
%e 6 | 6, 42, 66, 66, 66, 66, 66, 66, 66, ...
%e 7 | 7, 91, 308, 630, 1057, 1589, 2226, 2968, 3815, ...
%e 8 | 8, 136, 232, 232, 232, 232, 232, 232, 232, ...
%e 9 | 9, 288, 1305, 2808, 4581, 6624, 8937, 11520, 14373, ...
%e 10 | 10, 390, 900, 1050, 1200, 1350, 1500, 1650, 1800, ...
%e 11 | 11, 715, 3399, 7271, 11803, 16995, 22847, 29359, 36531, ...
%e 12 | 12, 756, 1428, 1428, 1428, 1428, 1428, 1428, 1428, ...
%e 13 | 13, 1508, 9061, 22243, 38350, 57382, 79339, 104221, 132028, ...
%e 14 | 14, 1722, 4704, 6174, 7644, 9114, 10584, 12054, 13524, ...
%e 15 | 15, 2835, 15345, 35880, 62370, 94035, 130875, 172890, 220080, ...
%e 16 | 16, 3088, 9424, 12496, 14416, 16336, 18256, 20176, 22096, ...
%e 17 | 17, 4896, 30294, 77758, 141440, 220932, 316234, 427346, 554268, ...
%e 18 | 18, 4320, 11376, 16686, 21528, 25578, 29628, 33678, 37728, ...
%e 19 | 19, 7923, 48773, 122607, 218101, 335255, 474069, 634543, 816677, ...
%e 20 | 20, 8360, 30840, 48260, 60560, 72860, 85160, 97460, 109760, ...
%e 21 | 21, 12180, 66738, 153069, 260505, 389046, 538692, 709443, 901299, ...
%e 22 | 22, 12782, 49148, 79442, 100232, 121022, 141812, 162602, 183392, ...
%e .
%Y Cf. A350000 (n-gons), A350501 (vertices), A135565 (column 1), A349968 (column 2), A331450, A349967.
%K nonn,tabl
%O 3,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 01 2022