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

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, 22, 20, 16, 17, 24, 19, 14, 19, 25, 18, 20, 25, 24, 19, 24, 31, 27, 26, 24, 22, 32, 31, 28, 24, 29, 34, 30, 31, 37, 34, 34, 36, 35, 34, 35, 36, 43, 40, 36, 38, 37, 39, 40

Offset

0,2

Comments

Number of 1's in n-th row of triangle in A070887.

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

References

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.

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

Links

Vincenzo Librandi and N. J. A. Sloane, Table of n, a(n) for n = 0..10000 (First 1000 terms from Vincenzo Librandi)

Matthew Cook, A Concrete View of Rule 110 Computation, arXiv:0906.3248 [cs.CC], 2009.

Matthew Cook, Universality in Elementary Cellular Automata, Complex Systems 15 (2004), 1-40.

N. J. A. Sloane, Illustration of first 20 generations

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015

Eric Weisstein's World of Mathematics, Rule 110

Wikipedia, Rule 110

Index entries for sequences related to cellular automata

Formula

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

Maple

A071049 := proc(n)
    add( A070887(n+1, k), k=1..n+1) ;
end proc:
seq(A071049(n), n=0..20) ; # R. J. Mathar, Feb 18 2015

Mathematica

Total /@ CellularAutomaton[110, {{1}, 0}, 100] (* N. J. A. Sloane, Aug 10 2009 *)

Crossrefs

Cf. A070950, A070952, A070997, A071029, A071044, A151931, A246027.

Sequence in context: A119912 A076368 A279931 * A171637 A140187 A214127

Adjacent sequences: A071046 A071047 A071048 * A071050 A071051 A071052

Keyword

nonn

Author

Hans Havermann, May 26 2002

Extensions

Added references and links. - N. J. A. Sloane, Aug 09 2014

Changed offset to make consistent with A070952, etc. - N. J. A. Sloane, Aug 15 2014

Status

approved