A266377 Triangle read by rows giving successive states of cellular automaton generated by "Rule 21" initiated with a single ON (black) cell.

1, 0, 1, 1, 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..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 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=21; 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. A266379, A266380, A266216 (rows reversed).

Sequence in context: A113428 A133101 A258769 * A266326 A185295 A214295

Adjacent sequences: A266374 A266375 A266376 * A266378 A266379 A266380

Keyword

nonn,tabf,easy

Author

Robert Price, Dec 28 2015

Status

approved