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A294241
Longest non-repeating Game of Life on an n X n torus that ends with a fixed pattern.
0
2, 2, 3, 10, 52, 91, 224
OFFSET
1,1
COMMENTS
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
LINKS
Code Golf Stack Exchange User "Per Alexandersson", Longest non-repeating Game-of-Life sequence
EXAMPLE
For n = 3 the starting state is:
+---+---+---+
| * | * | * |
+---+---+---+
| | | |
+---+---+---+
| | | |
+---+---+---+
For n = 4 the starting state is:
+---+---+---+---+
| * | * | * | |
+---+---+---+---+
| | | * | |
+---+---+---+---+
| * | * | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
For n = 5 the starting state is:
+---+---+---+---+---+
| * | * | | * | |
+---+---+---+---+---+
| * | | | | |
+---+---+---+---+---+
| * | * | | * | * |
+---+---+---+---+---+
| * | | * | | |
+---+---+---+---+---+
| | | | | |
+---+---+---+---+---+
From Bert Dobbelaere, Jun 20 2024: (Start)
For n = 6 the starting state is:
+---+---+---+---+---+---+
| | | * | | * | * |
+---+---+---+---+---+---+
| * | * | | | * | * |
+---+---+---+---+---+---+
| | | * | | * | |
+---+---+---+---+---+---+
| * | * | | | | * |
+---+---+---+---+---+---+
| | | | | | * |
+---+---+---+---+---+---+
| | | | * | | * |
+---+---+---+---+---+---+
For n = 7 the starting state is:
+---+---+---+---+---+---+---+
| * | | * | * | | | * |
+---+---+---+---+---+---+---+
| * | | | * | | * | |
+---+---+---+---+---+---+---+
| | * | | * | * | | |
+---+---+---+---+---+---+---+
| | * | * | | | | * |
+---+---+---+---+---+---+---+
| | * | * | | * | * | |
+---+---+---+---+---+---+---+
| | | | | * | | * |
+---+---+---+---+---+---+---+
| | | * | | * | * | |
+---+---+---+---+---+---+---+ (End)
CROSSREFS
Sequence in context: A376723 A153920 A300483 * A067579 A019143 A084650
KEYWORD
nonn,more,hard
AUTHOR
Peter Kagey, Oct 25 2017
EXTENSIONS
a(7) from Bert Dobbelaere, Jun 20 2024
STATUS
approved