A266216 Triangle read by rows giving successive states of cellular automaton generated by "Rule 7" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

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

Mathematica

rule=7; 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. A266217, A266218, A266377 (rows reversed).

Sequence in context: A204269 A371690 A179830 * A025446 A373972 A266300

Adjacent sequences: A266213 A266214 A266215 * A266217 A266218 A266219

Keyword

nonn,tabf,easy

Author

Robert Price, Dec 24 2015

Status

approved