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A249668 Population of the n-th generation of the pattern 101//010 in the Life Without Death cellular automaton.

%I A249668 #22 Jun 13 2015 00:55:17
%S A249668 3,4,7,10,15,20,25,30,38,47,55,63,69,79,91,96,105,112,124,134,139,144,
%T A249668 152,157,163,168,176,183,187,195,205,217,223,229,239,247,259,273,285,
%U A249668 289,295,303,311,323,334,339,343,351,363,375,383,389,397,405,413,423
%N A249668 Population of the n-th generation of the pattern 101//010 in the Life Without Death cellular automaton.
%C A249668 Each generation, a cell turns on if it has exactly three neighbors that are on. Cells never turn off.
%C A249668 This pattern grows indefinitely. No other connected 3-celled pattern does so.
%H A249668 Eric M. Schmidt, <a href="/A249668/b249668.txt">Table of n, a(n) for n = 0..2500</a>
%H A249668 LifeWiki, <a href="http://www.conwaylife.com/wiki/Life_without_death">Life without death</a>
%H A249668 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1). (Initial terms do not obey recurrence; see formula section.)
%F A249668 For n >= 2108, a(n+6) = a(n) + 260. - _Eric M. Schmidt_, Nov 04 2014
%F A249668 For n >= 2115, a(n) = a(n-1) + a(n-6) - a(n-7). - _Eric M. Schmidt_, Nov 05 2014
%e A249668 Generation 0:
%e A249668 101
%e A249668 010
%e A249668 Generation 1:
%e A249668 111
%e A249668 010
%e A249668 Generation 2:
%e A249668 010
%e A249668 111
%e A249668 111
%e A249668 Generation 3:
%e A249668 111
%e A249668 111
%e A249668 111
%e A249668 010
%e A249668 Generation 4:
%e A249668 00100
%e A249668 01110
%e A249668 11111
%e A249668 01110
%e A249668 01110
%Y A249668 Cf. A097981, A151725, A151731.
%K A249668 nonn
%O A249668 0,1
%A A249668 _Eric M. Schmidt_, Nov 03 2014