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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 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.)