A357950 Maximum period of an elementary cellular automaton in a cyclic universe of width n.

2, 2, 6, 8, 30, 18, 126, 40, 504, 430, 979, 240, 1105, 2198, 6820, 6016, 78812, 7812, 183920, 142580, 352884, 122870, 3459591, 421188, 10828525, 334308, 81688176, 989212, 463347935, 5921860, 1211061438, 26636800, 3315517623, 187950912, 24752893585

Offset: 1

Author

Pontus von Brömssen, Oct 22 2022

Keywords

• nonn

Examples

			Examples of rules and initial states that give the maximum period:
   n   a(n) rule     initial state
  --------------------------------
   1     2    1                  0
   2     2    1                 00
   3     6   14                001
   4     8    3               0001
   5    30   45              00001
   6    18   45             000001
   7   126   45            0000001
   8    40   30           00000001
   9   504   45          000000001
  10   430   45         0000000001
  11   979   45        00000000001
  12   240   45       000000100001
  13  1105   45      0000000001011
  14  2198   45     00000000000001
  15  6820   75    000000000000001
  16  6016   30   0000000000000001
  17 78812   45  00000000000000001
  18  7812   75 000000000000000001
		

Links

• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton.
• Wikipedia, Elementary cellular automaton.
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A334499.

Formula

a(n) >= A334499(n). Equality holds (i.e., the maximum period can be achieved with a single cell initially on) for all n <= 35, except n = 12, 13, 23, 24, 25, 26, 28, 34.

Trivially a(n) <= 2^n. - Charles R Greathouse IV, Nov 09 2022

Extensions

a(19)-a(35) from Bert Dobbelaere, Oct 30 2022

Corrected a(23), a(25), a(26) and a(34) by Bert Dobbelaere, Nov 11 2022