A267520 Triangle read by rows giving successive states of cellular automaton generated by "Rule 139" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

This sequence is also generated by Rule 171.

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

Mathematica

rule=139; 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: A263919 A371689 A362129 * A114915 A360120 A361022

Adjacent sequences: A267517 A267518 A267519 * A267521 A267522 A267523

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 16 2016

Status

approved