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A071049 Number of 1's in n-th generation of 1-D CA using Rule 110, started with a single 1. 7
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 (list; graph; refs; listen; history; text; internal format)
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

Map[Function[Apply[Plus, Flatten[ #1]]], 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

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Last modified January 20 12:23 EST 2019. Contains 319330 sequences. (Running on oeis4.)