cp's OEIS Frontend

A294241 Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern.

%I A294241 #24 Jun 21 2024 03:54:35
%S A294241 2,2,3,10,52,91,224
%N A294241 Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern.
%C A294241 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 A294241 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 A294241 For n = 3 the starting state is:
%e A294241   +---+---+---+
%e A294241   | * | * | * |
%e A294241   +---+---+---+
%e A294241   |   |   |   |
%e A294241   +---+---+---+
%e A294241   |   |   |   |
%e A294241   +---+---+---+
%e A294241 For n = 4 the starting state is:
%e A294241   +---+---+---+---+
%e A294241   | * | * | * |   |
%e A294241   +---+---+---+---+
%e A294241   |   |   | * |   |
%e A294241   +---+---+---+---+
%e A294241   | * | * |   |   |
%e A294241   +---+---+---+---+
%e A294241   |   |   |   |   |
%e A294241   +---+---+---+---+
%e A294241 For n = 5 the starting state is:
%e A294241   +---+---+---+---+---+
%e A294241   | * | * |   | * |   |
%e A294241   +---+---+---+---+---+
%e A294241   | * |   |   |   |   |
%e A294241   +---+---+---+---+---+
%e A294241   | * | * |   | * | * |
%e A294241   +---+---+---+---+---+
%e A294241   | * |   | * |   |   |
%e A294241   +---+---+---+---+---+
%e A294241   |   |   |   |   |   |
%e A294241   +---+---+---+---+---+
%e A294241 From _Bert Dobbelaere_, Jun 20 2024: (Start)
%e A294241 For n = 6 the starting state is:
%e A294241   +---+---+---+---+---+---+
%e A294241   |   |   | * |   | * | * |
%e A294241   +---+---+---+---+---+---+
%e A294241   | * | * |   |   | * | * |
%e A294241   +---+---+---+---+---+---+
%e A294241   |   |   | * |   | * |   |
%e A294241   +---+---+---+---+---+---+
%e A294241   | * | * |   |   |   | * |
%e A294241   +---+---+---+---+---+---+
%e A294241   |   |   |   |   |   | * |
%e A294241   +---+---+---+---+---+---+
%e A294241   |   |   |   | * |   | * |
%e A294241   +---+---+---+---+---+---+
%e A294241 For n = 7 the starting state is:
%e A294241   +---+---+---+---+---+---+---+
%e A294241   | * |   | * | * |   |   | * |
%e A294241   +---+---+---+---+---+---+---+
%e A294241   | * |   |   | * |   | * |   |
%e A294241   +---+---+---+---+---+---+---+
%e A294241   |   | * |   | * | * |   |   |
%e A294241   +---+---+---+---+---+---+---+
%e A294241   |   | * | * |   |   |   | * |
%e A294241   +---+---+---+---+---+---+---+
%e A294241   |   | * | * |   | * | * |   |
%e A294241   +---+---+---+---+---+---+---+
%e A294241   |   |   |   |   | * |   | * |
%e A294241   +---+---+---+---+---+---+---+
%e A294241   |   |   | * |   | * | * |   |
%e A294241   +---+---+---+---+---+---+---+   (End)
%K A294241 nonn,more,hard
%O A294241 1,1
%A A294241 _Peter Kagey_, Oct 25 2017
%E A294241 a(7) from _Bert Dobbelaere_, Jun 20 2024