cp's OEIS Frontend

A071049 Number of 1's in n-th generation of 1-D CA using Rule 110, started with a single 1.

%I A071049 #61 Jun 16 2025 08:43:57
%S A071049 1,2,3,3,5,3,5,6,8,5,6,8,8,8,11,11,13,9,11,11,13,14,16,14,14,13,13,17,
%T A071049 22,20,16,17,24,19,14,19,25,18,20,25,24,19,24,31,27,26,24,22,32,31,28,
%U A071049 24,29,34,30,31,37,34,34,36,35,34,35,36,43,40,36,38,37,39,40
%N A071049 Number of 1's in n-th generation of 1-D CA using Rule 110, started with a single 1.
%C A071049 Number of 1's in n-th row of triangle in A070887.
%C A071049 Although the initial behavior is chaotic, it is an astonishing fact, pointed out by Wolfram [2002, p. 39], that after about three thousand terms all the irregularities disappear. - _N. J. A. Sloane_, May 15 2015
%D A071049 Matthew Cook, A Concrete View of Rule 110 Computation, in "The Complexity of Simple Programs", T. Neary, D. Woods, A. K. Seda, and N. Murphy (Eds.), 2008, pp. 31-55.
%D A071049 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071049 Vincenzo Librandi and N. J. A. Sloane, <a href="/A071049/b071049.txt">Table of n, a(n) for n = 0..10000</a> (First 1000 terms from Vincenzo Librandi)
%H A071049 Matthew Cook, <a href="https://arxiv.org/abs/0906.3248">A Concrete View of Rule 110 Computation</a>, arXiv:0906.3248 [cs.CC], 2009.
%H A071049 Matthew Cook, <a href="http://www.complex-systems.com/pdf/15-1-1.pdf">Universality in Elementary Cellular Automata</a>, Complex Systems 15 (2004), 1-40.
%H A071049 N. J. A. Sloane, <a href="/A071049/a071049_1.pdf">Illustration of first 20 generations</a>
%H A071049 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.
%H A071049 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule110.html">Rule 110</a>
%H A071049 Wikipedia, <a href="http://en.wikipedia.org/wiki/Rule_110">Rule 110</a>
%H A071049 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A071049 For n >= 2854, a(n+469) = -a(n+453) + a(n+256) + a(n+240) + a(n+229) + a(n+213) - a(n+16) - a(n). - _N. J. A. Sloane_, May 15 2015
%p A071049 A071049 := proc(n)
%p A071049     add( A070887(n+1,k),k=1..n+1) ;
%p A071049 end proc:
%p A071049 seq(A071049(n),n=0..20) ; # _R. J. Mathar_, Feb 18 2015
%t A071049 Total /@ CellularAutomaton[110,{{1},0},100] (* _N. J. A. Sloane_, Aug 10 2009 *)
%Y A071049 Cf. A070950, A070952, A070997, A071029, A071044, A151931, A246027.
%K A071049 nonn
%O A071049 0,2
%A A071049 _Hans Havermann_, May 26 2002
%E A071049 Added references and links. - _N. J. A. Sloane_, Aug 09 2014
%E A071049 Changed offset to make consistent with A070952, etc. - _N. J. A. Sloane_, Aug 15 2014