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a(n) is the number of active cells after a solid n X n square has reached a static state or constant population, closed and infinite loop in Conway's Game of Life.
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%I #7 Aug 04 2020 13:38:28

%S 0,4,12,0,24,8,12,0,52,8,12,0,4,8,0,56,72,40,60,0,52,24,92,48,28,96,

%T 312,40

%N a(n) is the number of active cells after a solid n X n square has reached a static state or constant population, closed and infinite loop in Conway's Game of Life.

%C Starting population for n is n^2.

%C a(n)=0 for n={1,4,8,12,15,20,..?..}, meaning that after a particular, finite number of generations, the grid is forever empty.

%C a(n) reaches a nonempty, single static state after a particular, finite number of generations for n={2,5,6,10,13,14,16,18,22,24,26,27,28,..?..}.

%C a(n) enters a constant population, infinite, two-state and closed loop after a particular, finite number of generations for n={3,7,9,11,17,19,21,23,25,..?..}.

%C For even generations > 153, a(29)=128. For odd generations > 153, a(29)=120. n=29 is the first value of a(n) for which the system enters a two-state loop with variable population after a particular, finite number of generations.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GameofLife.html">Game of Life</a>

%e a(5)=24 because a 5 X 5 solid square placed on an otherwise empty grid at generation 0 in Conway's Game of Life will enter a static state at generation 11 with 24 cells forever alive/active/on.

%K nonn,more

%O 1,2

%A Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 08 2004