A152389 - OEIS

%I #43 Nov 17 2021 11:55:05

%S 0,1,1,0,2,6,12,14,48,20,2,15,15,24,28,40,32,24,20,25,20,19,35,30,28,

%T 93,24,28,33,36,103,148,60,580,42,57,91,106,262,276,49,209,57,52,56,

%U 97,54,168,194,811,103,52,52,83,57,79,246,416,62,62,312,115,116

%N Number of steps in Conway's Game of Life for a row of n cells to stabilize.

%C A pattern is said to have stabilized if it consists entirely of a (possibly empty) periodic component and zero or more spaceships, such that the spaceships will never interact with each other or with the periodic part.

%H Eric M. Schmidt, <a href="/A152389/b152389.txt">Table of n, a(n) for n = 0..1000</a>

%H LifeWiki, <a href="https://www.conwaylife.com/wiki/One-cell-thick_pattern">One cell thick pattern</a>

%H Eric M. Schmidt, <a href="/A152389/a152389_3.cpp.txt">C++ code to compute this sequence</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GameofLife.html">Game of Life</a>

%e From _Eric M. Schmidt_, Aug 15 2012: (Start)

%e A 10-cell straight line evolves into a periodic pattern (the pentadecathlon) in two steps. Therefore a(10) = 2. (Based on example in A098720)

%e A 33-cell straight line evolves, in 387 steps, into a pattern consisting of a periodic component and four gliders. The pattern has not yet stabilized since the gliders will eventually collide.

%e A 56-cell straight line evolves, in 246 steps, into a pattern consisting of a periodic component and four gliders. The gliders will never collide with each other or with the periodic component, so the pattern has stabilized. Thus, a(56) = 246. (End)

%Y Cf. A098720, A152301.

%Y Cf. A061342.

%K nonn

%O 0,5

%A _N. J. A. Sloane_, Oct 23 2009, based on a posting by _Allan C. Wechsler_ to the Math Fun Mailing List.

%E More terms and definition changed by _Eric M. Schmidt_, Aug 15 2012