A267576 Triangle read by rows giving successive states of cellular automaton generated by "Rule 167" initiated with a single ON (black) cell.

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

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
                1 1 0
              1 1 0 1 0
            1 1 0 1 1 1 0
          1 1 0 1 0 1 0 1 0
        1 1 0 1 1 1 1 1 1 1 0
      1 1 0 1 0 1 1 1 1 1 0 1 0
    1 1 0 1 1 1 0 1 1 1 0 1 1 1 0
  1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
The full writeup of the rule has an infinite sequence of leading and trailing 1's from row 2 on:
00000000000000100000000000000
11111111111111101111111111111
11111111111111010111111111111
11111111111110111011111111111
11111111111101010101111111111
11111111111011111110111111111
11111111110101111101011111111
11111111101110111011101111111
11111111010101010101010111111
11111110111111111111111011111
11111101011111111111110101111
- R. J. Mathar, Aug 07 2025

Mathematica

rule=167; 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: A080909 A087755 A050072 * A156707 A131309 A267208

Adjacent sequences: A267573 A267574 A267575 * A267577 A267578 A267579

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 17 2016

Status

approved