A263428 Triangle read by rows giving successive states of cellular automaton generated by "Rule 3" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

This sequence is also generated by Rule 35.

Links

Robert Price, Table of n, a(n) for n = 0..9999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

The first ten rows:
                  1
                1 0 0
              0 0 0 1 0
            1 1 1 1 0 0 1
          0 0 0 0 0 0 1 0 0
        1 1 1 1 1 1 1 0 0 1 1
      0 0 0 0 0 0 0 0 0 1 0 0 0
    1 1 1 1 1 1 1 1 1 1 0 0 1 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1
Including leading and trailing 0's and 1's, the pattern is as follows:
00000000000000100000000000000
11111111111111001111111111111
00000000000000010000000000000
11111111111111100111111111111
00000000000000001000000000000
11111111111111110011111111111
00000000000000000100000000000
11111111111111111001111111111
00000000000000000010000000000
11111111111111111100111111111
00000000000000000001000000000
11111111111111111110011111111
00000000000000000000100000000
11111111111111111111001111111
- R. J. Mathar, Aug 07 2025

Mathematica

rule = 3; rows = 20; Flatten[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows - k + 1, rows + k - 1}], {k, 1, rows}]]

Crossrefs

Cf. A266068, A266069, A266070 (middle column), A260552 (rows reversed).

Sequence in context: A292438 A244525 A214263 * A016355 A016402 A016377

Adjacent sequences: A263425 A263426 A263427 * A263429 A263430 A263431

Keyword

nonn,tabf,easy

Author

Robert Price, Dec 20 2015

Status

approved