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%I #24 Jun 21 2024 03:54:35
%S 2,2,3,10,52,91,224
%N Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern.
%C We must have a(2n) >= a(n) because one can always place onto a 2n X 2n toroidal board four identical copies of a record-setting pattern for a(n), so that each copy of the pattern "thinks" that it is the sole occupant of an n X n toroidal board and thus acts accordingly. See also comments in A179412 for a related question about the longest repeating pattern on a toroidal board. - _Antti Karttunen_, Oct 30 2017
%H Code Golf Stack Exchange User "Per Alexandersson", <a href="https://codegolf.stackexchange.com/questions/9393/longest-non-repeating-game-of-life-sequence">Longest non-repeating Game-of-Life sequence</a>
%e For n = 3 the starting state is:
%e +---+---+---+
%e | * | * | * |
%e +---+---+---+
%e | | | |
%e +---+---+---+
%e | | | |
%e +---+---+---+
%e For n = 4 the starting state is:
%e +---+---+---+---+
%e | * | * | * | |
%e +---+---+---+---+
%e | | | * | |
%e +---+---+---+---+
%e | * | * | | |
%e +---+---+---+---+
%e | | | | |
%e +---+---+---+---+
%e For n = 5 the starting state is:
%e +---+---+---+---+---+
%e | * | * | | * | |
%e +---+---+---+---+---+
%e | * | | | | |
%e +---+---+---+---+---+
%e | * | * | | * | * |
%e +---+---+---+---+---+
%e | * | | * | | |
%e +---+---+---+---+---+
%e | | | | | |
%e +---+---+---+---+---+
%e From _Bert Dobbelaere_, Jun 20 2024: (Start)
%e For n = 6 the starting state is:
%e +---+---+---+---+---+---+
%e | | | * | | * | * |
%e +---+---+---+---+---+---+
%e | * | * | | | * | * |
%e +---+---+---+---+---+---+
%e | | | * | | * | |
%e +---+---+---+---+---+---+
%e | * | * | | | | * |
%e +---+---+---+---+---+---+
%e | | | | | | * |
%e +---+---+---+---+---+---+
%e | | | | * | | * |
%e +---+---+---+---+---+---+
%e For n = 7 the starting state is:
%e +---+---+---+---+---+---+---+
%e | * | | * | * | | | * |
%e +---+---+---+---+---+---+---+
%e | * | | | * | | * | |
%e +---+---+---+---+---+---+---+
%e | | * | | * | * | | |
%e +---+---+---+---+---+---+---+
%e | | * | * | | | | * |
%e +---+---+---+---+---+---+---+
%e | | * | * | | * | * | |
%e +---+---+---+---+---+---+---+
%e | | | | | * | | * |
%e +---+---+---+---+---+---+---+
%e | | | * | | * | * | |
%e +---+---+---+---+---+---+---+ (End)
%K nonn,more,hard
%O 1,1
%A _Peter Kagey_, Oct 25 2017
%E a(7) from _Bert Dobbelaere_, Jun 20 2024
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