%I #24 Jun 21 2024 03:54:35
%S 2,2,3,10,52,91,224
%N Longest nonrepeating 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 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
%H Code Golf Stack Exchange User "Per Alexandersson", <a href="https://codegolf.stackexchange.com/questions/9393/longestnonrepeatinggameoflifesequence">Longest nonrepeating GameofLife 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
