

A294241


Longest nonrepeating Game of Life on an n X n torus that ends with a fixed pattern.


0




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 recordsetting 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

Table of n, a(n) for n=1..6.
Stack Exchange User "Per Alexandersson", Longest nonrepeating GameofLife sequence


EXAMPLE

For n = 3 the starting state is:
++++
 *  *  * 
++++
   
++++
   
++++
For n = 4 the starting state is:
+++++
 *  *  *  
+++++
   *  
+++++
 *  *   
+++++
    
+++++
For n = 5 the starting state is:
++++++
 *  *   *  
++++++
 *     
++++++
 *  *   *  * 
++++++
 *   *   
++++++
     
++++++


CROSSREFS

Sequence in context: A338372 A153920 A300483 * A067579 A019143 A084650
Adjacent sequences: A294238 A294239 A294240 * A294242 A294243 A294244


KEYWORD

nonn,more,hard


AUTHOR

Peter Kagey, Oct 25 2017


STATUS

approved



