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%I #19 Jan 05 2024 12:56:38
%S 3,3,4,3,5,5,3,5,10,6,3,5,15,19,7,3,5,20,25,42,8,3,5,25,25,119,57,9,3,
%T 5,30,25,231,81,135,10,3,5,35,25,378,81,504,171,11,3,5,40,25,560,81,
%U 1017,311,341,12,3,5,45,25,777,81,1620,361,1309,313,13
%N Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of vertices in a regular n-gon after k generations of mitosis.
%C See A350000 for further details and images of the n-gons.
%H Scott R. Shannon, <a href="/A350501/a350501_5.png">Illustration of T(10,1)</a>.
%H Scott R. Shannon, <a href="/A350501/a350501_4.png">Illustration of T(10,2)</a>.
%H Scott R. Shannon, <a href="/A350501/a350501.png">Illustration of T(10,3)</a>.
%H Scott R. Shannon, <a href="/A350501/a350501_3.png">Illustration of T(11,1)</a>.
%H Scott R. Shannon, <a href="/A350501/a350501_2.png">Illustration of T(11,2)</a>.
%H Scott R. Shannon, <a href="/A350501/a350501_1.png">Illustration of T(11,3)</a>.
%e The table begins:
%e .
%e | Number of vertices after k generations
%e n\k | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
%e ----------------------------------------------------------------------------------
%e 3 | 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...
%e 4 | 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, ...
%e 5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
%e 6 | 6, 19, 25, 25, 25, 25, 25, 25, 25, 25, ...
%e 7 | 7, 42, 119, 231, 378, 560, 777, 1029, 1316, 1638, ...
%e 8 | 8, 57, 81, 81, 81, 81, 81, 81, 81, 81, ...
%e 9 | 9, 135, 504, 1017, 1620, 2313, 3096, 3969, 4932, 5985, ...
%e 10 | 10, 171, 311, 361, 411, 461, 511, 561, 611, 661, ...
%e 11 | 11, 341, 1309, 2629, 4169, 5929, 7909, 10109, 12529, 1516, ...
%e 12 | 12, 313, 481, 481, 481, 481, 481, 481, 481, 481, ...
%e 13 | 13, 728, 3601, 8125, 13624, 20098, 27547, 35971, 45370, 55744, ...
%e 14 | 14, 771, 1639, 2129, 2619, 3109, 3599, 4089, 4579, 5069, ...
%e 15 | 15, 1380, 5985, 13125, 22185, 32970, 45480, 59715, 75675, 93360, ...
%e 16 | 16, 1393, 3329, 4257, 4897, 5537, 6177, 6817, 7457, 8097, ...
%e 17 | 17, 2397, 12070, 28628, 50558, 77758, 110228, 147968, 190978, 239258, ...
%e 18 | 18, 1855, 4033, 5815, 7363, 8713, 10063, 11413, 12763, 14113, ...
%e 19 | 19, 3895, 19418, 44992, 77786, 117800, 165034, 219488, 281162, 350056, ...
%e 20 | 20, 3861, 11261, 16641, 20741, 24841, 28941, 33041, 37141, 41241, ...
%e 21 | 21, 6006, 26019, 55734, 92484, 136269, 187089, 244944, 309834, 381759, ...
%e 22 | 22, 5963, 18107, 27413, 34343, 41273, 48203, 55133, 62063, 68993, ...
%e .
%Y Cf. A350000 (n-gons), A350502 (edges), A007569 (column 1), A349967 (column 2), A331450, A349968.
%K nonn,tabl
%O 3,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 01 2022
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