A267129 Triangle read by rows giving successive states of cellular automaton generated by "Rule 101" initiated with a single ON (black) cell.

1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0

Offset

0

Comments

Row n has length 2n+1.

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

Mathematica

rule=101; 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: A156728 A361023 A267442 * A267848 A267179 A244527

Adjacent sequences: A267126 A267127 A267128 * A267130 A267131 A267132

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 10 2016

Status

approved