|
%I #3 Aug 08 2015 23:49:09
%S 0,0,1,12,43,163,8424,582769,40292074
%N Number of n X n Life configurations that are "flip-flops" (Life cycles of period 2).
%C These counts have not been reduced to take account of the symmetries of the board.
%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982; see Chapter 25.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%e The 12 solutions for n=4 belong to four isomorphism classes under symmetry:
%e The blinker, four cases:
%e ..State 1. ..State 2.
%e .......... ....*.....
%e ...***.... ....*.....
%e .......... ....*.....
%e .......... ..........
%e The toad, four cases:
%e ..State 1. ..State 2.
%e .....*.... ..........
%e ...*..*... ....***...
%e ...*..*... ...***....
%e ....*..... ..........
%e The beacon, two cases:
%e ..State 1. ..State 2.
%e .....**... .....**...
%e ......*... .....**...
%e ...*...... ...**.....
%e ...**..... ...**.....
%e The clock, two cases:
%e ..State 1. ..State 2.
%e .....*.... ....*.....
%e ...*.*.... .....**...
%e ....*.*... ...**.....
%e ....*..... .....*....
%Y Cf. A134963, A136278, A136280.
%K nonn
%O 1,4
%A _Don Knuth_, Mar 26 2008
|
