

A164936


Population in generation n of the following pattern in Conway's Game of Life: 00000010 00001011 00001010 00001000 00100000 10100000, where "1" is a live cell and "0" is a dead cell, and spaces indicate a line break.


1



10, 14, 13, 19, 16, 21, 20, 26, 24, 28, 30, 26, 34, 32, 29, 36, 22, 19, 18, 19, 21, 22, 26, 27, 38, 38, 46, 52, 54, 55, 58, 58, 51, 63, 38, 43, 36, 38, 41, 42, 39, 38, 36, 42, 47, 58, 60, 56, 55, 53, 60, 57, 62, 51, 49, 59, 45, 36, 34, 35, 35, 39, 36, 35, 36
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OFFSET

0,1


COMMENTS

Because the pattern never stabilizes, the sequence will continue to grow. With 10 cells in its initial state, this is the smallest pattern that grows indefinitely in Conway's Game of Life.
Because this pattern evolves into a blocklaying switch engine, some blinkers, a glider and some still lifes, the first differences of this sequence eventually (i.e., after about 600 generations) has period 288.  Nathaniel Johnston, May 15 2011


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 0..1500
LifeWiki, Blocklaying switch engine
LifeWiki, Infinite growth
Eric M. Schmidt, C++ code to compute this sequence
Index entries for sequences related to cellular automata
Index entries for linear recurrences with constant coefficients, order 145.


FORMULA

For n >= 708, a(n) = a(n144) + 16. Hence, a(n) ~ n/9.  Eric M. Schmidt, Mar 10 2013


EXAMPLE

The pattern laid out graphically:
00000010
00001011
00001010
00001000
00100000
10100000
After 25 generations the population is 38, so a(25)=38.


MATHEMATICA

a[n_] :=
Total[CellularAutomaton[{224, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2,
2}}}, {1,
1}}, {{{0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 1, 1}, {0, 0,
0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0,
0, 0}, {1, 0, 1, 0, 0, 0, 0, 0}}, {{0}}}, {{n}}], Infinity]


CROSSREFS

Sequence in context: A072146 A074674 A241041 * A102361 A280032 A227010
Adjacent sequences: A164933 A164934 A164935 * A164937 A164938 A164939


KEYWORD

nonn


AUTHOR

Ben Branman, Aug 31 2009


EXTENSIONS

Extended by Nathaniel Johnston, May 15 2011


STATUS

approved



