A266669 Triangle read by rows giving successive states of cellular automaton generated by "Rule 53" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

Links

Robert Price, Table of n, a(n) for n = 0..10000

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

Mathematica

rule=53; 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. A266670, A266671, A266605 (rows reversed).

Sequence in context: A128937 A288004 A102511 * A129360 A129372 A169591

Adjacent sequences: A266666 A266667 A266668 * A266670 A266671 A266672

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 02 2016

Status

approved