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.

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, 3, 8, 80, 66, 630, 232, 288, 10, 3, 8, 95, 66, 1057, 232, 1305, 390, 11, 3, 8, 110, 66, 1589, 232, 2808, 900, 715, 12, 3, 8, 125, 66, 2226, 232, 4581, 1050, 3399, 756, 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.

Example

The table begins:
.
      |               Number of edges after k generations
  n\k |  0,     1,     2,      3,      4,      5,      6,      7,      8, ...
----------------------------------------------------------------------------------
   3  |  3,     3,     3,      3,      3,      3,      3,      3,      3, ...
   4  |  4,     8,     8,      8,      8,      8,      8,      8,      8, ...
   5  |  5,    20,    35,     50,     65,     80,     95,    110,    125, ...
   6  |  6,    42,    66,     66,     66,     66,     66,     66,     66, ...
   7  |  7,    91,   308,    630,   1057,   1589,   2226,   2968,   3815, ...
   8  |  8,   136,   232,    232,    232,    232,    232,    232,    232, ...
   9  |  9,   288,  1305,   2808,   4581,   6624,   8937,  11520,  14373, ...
  10  | 10,   390,   900,   1050,   1200,   1350,   1500,   1650,   1800, ...
  11  | 11,   715,  3399,   7271,  11803,  16995,  22847,  29359,  36531, ...
  12  | 12,   756,  1428,   1428,   1428,   1428,   1428,   1428,   1428, ...
  13  | 13,  1508,  9061,  22243,  38350,  57382,  79339, 104221, 132028, ...
  14  | 14,  1722,  4704,   6174,   7644,   9114,  10584,  12054,  13524, ...
  15  | 15,  2835, 15345,  35880,  62370,  94035, 130875, 172890, 220080, ...
  16  | 16,  3088,  9424,  12496,  14416,  16336,  18256,  20176,  22096, ...
  17  | 17,  4896, 30294,  77758, 141440, 220932, 316234, 427346, 554268, ...
  18  | 18,  4320, 11376,  16686,  21528,  25578,  29628,  33678,  37728, ...
  19  | 19,  7923, 48773, 122607, 218101, 335255, 474069, 634543, 816677, ...
  20  | 20,  8360, 30840,  48260,  60560,  72860,  85160,  97460, 109760, ...
  21  | 21, 12180, 66738, 153069, 260505, 389046, 538692, 709443, 901299, ...
  22  | 22, 12782, 49148,  79442, 100232, 121022, 141812, 162602, 183392, ...
.

Crossrefs

Cf. A350000 (n-gons), A350501 (vertices), A135565 (column 1), A349968 (column 2), A331450, A349967.

Sequence in context: A027011 A339400 A267048 * A326401 A326415 A343443

Adjacent sequences: A350499 A350500 A350501 * A350503 A350504 A350505

Keyword

nonn,tabl

Author

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

Status

approved