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A267679 Triangle read by rows giving successive states of cellular automaton generated by "Rule 201" initiated with a single ON (black) cell. 4
1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

Row n has length 2n+1.

The fact that only n cells to the left and right of the initially active cell are updated at step n is contradictory to the usual treatment of a "Rule m" automaton, where all cells are updated depending on their neighborhood. See also the illustration of "Rule 201" on the MathWorld page. - M. F. Hasler, Jul 28 2018

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

EXAMPLE

The first ten rows:

                  1

                0 0 0

              1 0 1 0 1

            1 1 0 0 0 1 1

          1 1 1 0 1 0 1 1 1

        1 1 1 1 0 0 0 1 1 1 1

      1 1 1 1 1 0 1 0 1 1 1 1 1

    1 1 1 1 1 1 0 0 0 1 1 1 1 1 1

  1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1

MATHEMATICA

rule=201; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

PROG

(PARI) A267679_row(n)=if(n==1, [0, 0, 0], binary(1<<(n*2+1)-(bittest(n, 0)*2+5)<<(n-1)-1)) \\ M. F. Hasler, Jul 28 2018

CROSSREFS

Cf. A267681 (value of row n read as binary number). - M. F. Hasler, Jul 28 2018

Sequence in context: A089011 A267043 A266444 * A267868 A288733 A095111

Adjacent sequences:  A267676 A267677 A267678 * A267680 A267681 A267682

KEYWORD

nonn,tabf,easy

AUTHOR

Robert Price, Jan 19 2016

STATUS

approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)