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

3,1

Comments

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

Links

Table of n, a(n) for n=3..68.

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).

Example

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, ...
.

Crossrefs

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

Sequence in context: A138372 A316662 A123708 * A102302 A130896 A254279

Adjacent sequences: A350498 A350499 A350500 * A350502 A350503 A350504

Keyword

nonn,tabl

Author

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

Status

approved