A099733 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.

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, 312, 40

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

Starting population for n is n^2.

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.

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,..?..}.

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,..?..}.

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.

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Game of Life