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A267708 Triangle read by rows giving successive states of cellular automaton generated by "Rule 206" initiated with a single ON (black) cell. 1
1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

Row n has length 2n+1.

This sequence is also generated by Rule 238.

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

FORMULA

Conjecture: a(n) = (1 + (-1)^floor(2*sqrt(n)))/2. - Velin Yanev, Nov 30 2016

EXAMPLE

The first ten rows:

                  1

                1 1 0

              1 1 1 0 0

            1 1 1 1 0 0 0

          1 1 1 1 1 0 0 0 0

        1 1 1 1 1 1 0 0 0 0 0

      1 1 1 1 1 1 1 0 0 0 0 0 0

    1 1 1 1 1 1 1 1 0 0 0 0 0 0 0

  1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

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

MATHEMATICA

rule=206; 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 *)

CROSSREFS

Sequence in context: A060038 A197774 A219009 * A167021 A267687 A304653

Adjacent sequences:  A267705 A267706 A267707 * A267709 A267710 A267711

KEYWORD

nonn,tabf,easy

AUTHOR

Robert Price, Jan 19 2016

STATUS

approved

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Last modified August 6 15:36 EDT 2020. Contains 336252 sequences. (Running on oeis4.)