A332717 Triangle read by rows in which row n lists the possible eventual periods of cellular automaton rule 110 in a cyclic universe of width n.

1, 1, 1, 1, 2, 1, 1, 9, 1, 14, 1, 2, 8, 16, 1, 3, 7, 1, 5, 15, 25, 1, 7, 110, 1, 2, 9, 18, 1, 351, 1, 7, 12, 14, 21, 91, 1, 295, 1, 2, 8, 16, 24, 32, 1, 7, 119, 578, 1, 3, 7, 9, 27, 81, 1, 190, 285, 1, 2, 5, 7, 15, 25, 30, 50, 200, 240, 1, 14, 21, 189, 315, 630

Offset: 1

Author

Hans Havermann, Jun 08 2020

Keywords

• nonn
• tabf
• hard
• more

Comments

Frequency of occurrence for the first 73 terms (semicolons separate rows): 2; 4; 8; 4, 12; 32; 10, 54; 9, 119; 20, 12, 8, 216; 17, 18, 477; 134, 220, 130, 540; 35, 495, 1518; 34, 12, 3426, 624; 54, 8138; 67, 8442, 644, 371, 168, 6692; 113, 32655; 116, 12, 8, 680, 1920, 62800; 138, 93330, 15895, 21709; 181, 36, 2349, 57024, 198594, 3960; 249, 28481, 495558; 534, 12, 3040, 49700, 270, 3300, 614140, 30660, 342380, 4540; 414, 455, 42, 7938, 331590, 1756713. Note that the sum of the frequencies of row n is 2^n.

Examples

			Triangle begins:
  1
  1
  1
  1    2
  1
  1    9
  1   14
  1    2    8   16
  1    3    7
  1    5   15   25
  1    7  110
  1    2    9   18
  1  351
  1    7   12   14   21   91
  1  295
  1    2    8   16   24   32
  1    7  119  578
  1    3    7    9   27   81
  1  190  285
  1    2    5    7   15   25   30   50  200  240
  1   14   21  189  315  630
		

Crossrefs

Cf. A332718 (row lengths), A204371 (final terms for each row).