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%I #23 Nov 11 2022 07:04:50
%S 2,2,6,8,30,18,126,40,504,430,979,240,1105,2198,6820,6016,78812,7812,
%T 183920,142580,352884,122870,3459591,421188,10828525,334308,81688176,
%U 989212,463347935,5921860,1211061438,26636800,3315517623,187950912,24752893585
%N Maximum period of an elementary cellular automaton in a cyclic universe of width n.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Elementary_cellular_automaton">Elementary cellular automaton</a>.
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F 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.
%F Trivially a(n) <= 2^n. - _Charles R Greathouse IV_, Nov 09 2022
%e Examples of rules and initial states that give the maximum period:
%e n a(n) rule initial state
%e --------------------------------
%e 1 2 1 0
%e 2 2 1 00
%e 3 6 14 001
%e 4 8 3 0001
%e 5 30 45 00001
%e 6 18 45 000001
%e 7 126 45 0000001
%e 8 40 30 00000001
%e 9 504 45 000000001
%e 10 430 45 0000000001
%e 11 979 45 00000000001
%e 12 240 45 000000100001
%e 13 1105 45 0000000001011
%e 14 2198 45 00000000000001
%e 15 6820 75 000000000000001
%e 16 6016 30 0000000000000001
%e 17 78812 45 00000000000000001
%e 18 7812 75 000000000000000001
%Y Cf. A334499.
%K nonn
%O 1,1
%A _Pontus von Brömssen_, Oct 22 2022
%E a(19)-a(35) from _Bert Dobbelaere_, Oct 30 2022
%E Corrected a(23), a(25), a(26) and a(34) by _Bert Dobbelaere_, Nov 11 2022