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A357950 Maximum period of an elementary cellular automaton in a cyclic universe of width n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton.
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
EXAMPLE
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
CROSSREFS
Cf. A334499.
Sequence in context: A079494 A169970 A334499 * A201499 A346201 A131553
KEYWORD
nonn
AUTHOR
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
STATUS
approved

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Last modified May 17 23:39 EDT 2024. Contains 372608 sequences. (Running on oeis4.)