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A266982 Triangle read by rows giving successive states of cellular automaton generated by "Rule 81" initiated with a single ON (black) cell. 3
1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 113.

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(0)=1; for n>0, a(n) = ( Sum_{i=1..n-2} floor((n-2)/i) ) mod 2. - Wesley Ivan Hurt, Mar 22 2016

EXAMPLE

The first ten rows:

                  1

                0 0 1

              1 1 0 0 0

            0 0 1 1 1 1 1

          1 1 0 0 0 0 0 0 0

        0 0 1 1 1 1 1 1 1 1 1

      1 1 0 0 0 0 0 0 0 0 0 0 0

    0 0 1 1 1 1 1 1 1 1 1 1 1 1 1

  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

MATHEMATICA

rule=81; 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: A188398 A288929 A285083 * A051341 A057211 A120531

Adjacent sequences:  A266979 A266980 A266981 * A266983 A266984 A266985

KEYWORD

nonn,tabf,easy

AUTHOR

Robert Price, Jan 07 2016

STATUS

approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)