A350501 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.

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, 5, 30, 25, 231, 81, 135, 10, 3, 5, 35, 25, 378, 81, 504, 171, 11, 3, 5, 40, 25, 560, 81, 1017, 311, 341, 12, 3, 5, 45, 25, 777, 81, 1620, 361, 1309, 313, 13

Offset: 3

Author

Scott R. Shannon and N. J. A. Sloane, Jan 01 2022

Keywords

• nonn
• tabl

Comments

See A350000 for further details and images of the n-gons.

Examples

			The table begins:
.
      |               Number of vertices after k generations
  n\k |  0,    1,     2,     3,     4,      5,      6,      7,      8,      9, ...
----------------------------------------------------------------------------------
   3  |  3,    3,     3,     3,     3,      3,      3,      3,      3,      3, ...
   4  |  4,    5,     5,     5,     5,      5,      5,      5,      5,      5, ...
   5  |  5,   10,    15,    20,    25,     30,     35,     40,     45,     50, ...
   6  |  6,   19,    25,    25,    25,     25,     25,     25,     25,     25, ...
   7  |  7,   42,   119,   231,   378,    560,    777,   1029,   1316,   1638, ...
   8  |  8,   57,    81,    81,    81,     81,     81,     81,     81,     81, ...
   9  |  9,  135,   504,  1017,  1620,   2313,   3096,   3969,   4932,   5985, ...
  10  | 10,  171,   311,   361,   411,    461,    511,    561,    611,    661, ...
  11  | 11,  341,  1309,  2629,  4169,   5929,   7909,  10109,  12529,   1516, ...
  12  | 12,  313,   481,   481,   481,    481,    481,    481,    481,    481, ...
  13  | 13,  728,  3601,  8125, 13624,  20098,  27547,  35971,  45370,  55744, ...
  14  | 14,  771,  1639,  2129,  2619,   3109,   3599,   4089,   4579,   5069, ...
  15  | 15, 1380,  5985, 13125, 22185,  32970,  45480,  59715,  75675,  93360, ...
  16  | 16, 1393,  3329,  4257,  4897,   5537,   6177,   6817,   7457,   8097, ...
  17  | 17, 2397, 12070, 28628, 50558,  77758, 110228, 147968, 190978, 239258, ...
  18  | 18, 1855,  4033,  5815,  7363,   8713,  10063,  11413,  12763,  14113, ...
  19  | 19, 3895, 19418, 44992, 77786, 117800, 165034, 219488, 281162, 350056, ...
  20  | 20, 3861, 11261, 16641, 20741,  24841,  28941,  33041,  37141,  41241, ...
  21  | 21, 6006, 26019, 55734, 92484, 136269, 187089, 244944, 309834, 381759, ...
  22  | 22, 5963, 18107, 27413, 34343,  41273,  48203,  55133,  62063,  68993, ...
.
		

Links

• Scott R. Shannon, Illustration of T(10,1).
• Scott R. Shannon, Illustration of T(10,2).
• Scott R. Shannon, Illustration of T(10,3).
• Scott R. Shannon, Illustration of T(11,1).
• Scott R. Shannon, Illustration of T(11,2).
• Scott R. Shannon, Illustration of T(11,3).

Crossrefs

Cf. A350000 (n-gons), A350502 (edges), A007569 (column 1), A349967 (column 2), A331450, A349968.