A249668 - OEIS

%I #22 Jun 13 2015 00:55:17

%S 3,4,7,10,15,20,25,30,38,47,55,63,69,79,91,96,105,112,124,134,139,144,

%T 152,157,163,168,176,183,187,195,205,217,223,229,239,247,259,273,285,

%U 289,295,303,311,323,334,339,343,351,363,375,383,389,397,405,413,423

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

%C Each generation, a cell turns on if it has exactly three neighbors that are on. Cells never turn off.

%C This pattern grows indefinitely. No other connected 3-celled pattern does so.

%H Eric M. Schmidt, <a href="/A249668/b249668.txt">Table of n, a(n) for n = 0..2500</a>

%H LifeWiki, <a href="http://www.conwaylife.com/wiki/Life_without_death">Life without death</a>

%H <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 For n >= 2108, a(n+6) = a(n) + 260. - _Eric M. Schmidt_, Nov 04 2014

%F For n >= 2115, a(n) = a(n-1) + a(n-6) - a(n-7). - _Eric M. Schmidt_, Nov 05 2014

%e Generation 0:

%e 101

%e 010

%e Generation 1:

%e 111

%e 010

%e Generation 2:

%e 010

%e 111

%e 111

%e Generation 3:

%e 111

%e 111

%e 111

%e 010

%e Generation 4:

%e 00100

%e 01110

%e 11111

%e 01110

%e 01110

%Y Cf. A097981, A151725, A151731.

%K nonn

%O 0,1

%A _Eric M. Schmidt_, Nov 03 2014