A267417 Triangle read by rows giving successive states of cellular automaton generated by "Rule 129" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

This sequence is also generated by Rule 161.

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
              0 0 1 0 0
            0 0 0 0 0 0 0
          0 0 1 1 1 1 1 0 0
        0 0 0 0 1 1 1 0 0 0 0
      0 0 1 1 0 0 1 0 0 1 1 0 0
    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 0 0
0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
The full writeup, including the leading and trailing infinite sequences of 1's starts:
00000000000000100000000000000
11111111111110001111111111111
11111111111100100111111111111
11111111111000000011111111111
11111111110011111001111111111
11111111100001110000111111111
11111111001100100110011111111
11111110000000000000001111111
11111100111111111111100111111
11111000011111111111000011111
11110011001111111110011001111
- R. J. Mathar, Aug 07 2025

Mathematica

rule=129; 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: A015269 A016347 A015989 * A014189 A319691 A079979

Adjacent sequences: A267414 A267415 A267416 * A267418 A267419 A267420

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 14 2016

Status

approved