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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 (list; graph; refs; listen; history; text; internal format)
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 block-laying 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, Block-laying 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(n-144) + 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

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Last modified April 23 22:58 EDT 2019. Contains 322389 sequences. (Running on oeis4.)