A265186 Triangle read by rows giving successive states of cellular automaton generated by "Rule 175" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

Although the start of this sequence is similar to that of A070200 and A226520, after a while these three sequences are completely different. - N. J. A. Sloane, Jan 18 2016

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 1
            1 1 0 1 1 1 1
          1 1 0 1 1 1 1 1 1
        1 1 0 1 1 1 1 1 1 1 1
      1 1 0 1 1 1 1 1 1 1 1 1 1
    1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
The full array including leading and trailing 1's is:
00000000000000100000000000000
11111111111111101111111111111
11111111111111011111111111111
11111111111110111111111111111
11111111111101111111111111111
11111111111011111111111111111
11111111110111111111111111111
11111111101111111111111111111
11111111011111111111111111111
11111110111111111111111111111
11111101111111111111111111111
11111011111111111111111111111
11110111111111111111111111111
11101111111111111111111111111
- R. J. Mathar, Aug 08 2025

Mathematica

rule=175; 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

Cf. A262779, A198694, A266678 (central column), A267922 (rows reversed).

Not the same: A070200, A226520.

Sequence in context: A261092 A285960 A174600 * A248392 A188318 A361897

Adjacent sequences: A265183 A265184 A265185 * A265187 A265188 A265189

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 18 2016

Status

approved