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A350502 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.

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%I A350502 #15 Jan 05 2024 12:50:13
%S A350502 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 A350502 3,8,80,66,630,232,288,10,3,8,95,66,1057,232,1305,390,11,3,8,110,66,
%U A350502 1589,232,2808,900,715,12,3,8,125,66,2226,232,4581,1050,3399,756,13
%N A350502 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 A350502 See A350000 for further details and images of the n-gons.
%e A350502 The table begins:
%e A350502 .
%e A350502       |               Number of edges after k generations
%e A350502   n\k |  0,     1,     2,      3,      4,      5,      6,      7,      8, ...
%e A350502 ----------------------------------------------------------------------------------
%e A350502    3  |  3,     3,     3,      3,      3,      3,      3,      3,      3, ...
%e A350502    4  |  4,     8,     8,      8,      8,      8,      8,      8,      8, ...
%e A350502    5  |  5,    20,    35,     50,     65,     80,     95,    110,    125, ...
%e A350502    6  |  6,    42,    66,     66,     66,     66,     66,     66,     66, ...
%e A350502    7  |  7,    91,   308,    630,   1057,   1589,   2226,   2968,   3815, ...
%e A350502    8  |  8,   136,   232,    232,    232,    232,    232,    232,    232, ...
%e A350502    9  |  9,   288,  1305,   2808,   4581,   6624,   8937,  11520,  14373, ...
%e A350502   10  | 10,   390,   900,   1050,   1200,   1350,   1500,   1650,   1800, ...
%e A350502   11  | 11,   715,  3399,   7271,  11803,  16995,  22847,  29359,  36531, ...
%e A350502   12  | 12,   756,  1428,   1428,   1428,   1428,   1428,   1428,   1428, ...
%e A350502   13  | 13,  1508,  9061,  22243,  38350,  57382,  79339, 104221, 132028, ...
%e A350502   14  | 14,  1722,  4704,   6174,   7644,   9114,  10584,  12054,  13524, ...
%e A350502   15  | 15,  2835, 15345,  35880,  62370,  94035, 130875, 172890, 220080, ...
%e A350502   16  | 16,  3088,  9424,  12496,  14416,  16336,  18256,  20176,  22096, ...
%e A350502   17  | 17,  4896, 30294,  77758, 141440, 220932, 316234, 427346, 554268, ...
%e A350502   18  | 18,  4320, 11376,  16686,  21528,  25578,  29628,  33678,  37728, ...
%e A350502   19  | 19,  7923, 48773, 122607, 218101, 335255, 474069, 634543, 816677, ...
%e A350502   20  | 20,  8360, 30840,  48260,  60560,  72860,  85160,  97460, 109760, ...
%e A350502   21  | 21, 12180, 66738, 153069, 260505, 389046, 538692, 709443, 901299, ...
%e A350502   22  | 22, 12782, 49148,  79442, 100232, 121022, 141812, 162602, 183392, ...
%e A350502 .
%Y A350502 Cf. A350000 (n-gons), A350501 (vertices), A135565 (column 1), A349968 (column 2), A331450, A349967.
%K A350502 nonn,tabl
%O A350502 3,1
%A A350502 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 01 2022