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

1,2

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.

Links

Table of n, a(n) for n=1..28.

Eric Weisstein's World of Mathematics, Game of Life

Example

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.

Crossrefs

Sequence in context: A354777 A218858 A014458 * A350259 A330989 A073902

Adjacent sequences: A099730 A099731 A099732 * A099734 A099735 A099736

Keyword

nonn,more

Author

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

Status

approved