A266298 Triangle read by rows giving successive states of cellular automaton generated by "Rule 14" initiated with a single ON (black) cell.

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

Offset

0

Comments

Row n has length 2n+1.

This sequence is also generated by Rules 46, 142 and 174.

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

Mathematica

rule=14; 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. A164908, A266299, A267006 (row reverse).

Sequence in context: A348292 A127243 A127248 * A265695 A116938 A105589

Adjacent sequences: A266295 A266296 A266297 * A266299 A266300 A266301

Keyword

nonn,tabf,easy

Author

Robert Price, Dec 26 2015

Status

approved