A266300 Triangle read by rows giving successive states of cellular automaton generated by "Rule 15" initiated with a single ON (black) cell.

1, 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

Offset

0

Comments

Row n has length 2n+1.

References

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

Links

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

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

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 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 0

Mathematica

rule=15; 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

Sequence in context: A266216 A025446 A373972 * A266605 A016421 A014030

Adjacent sequences: A266297 A266298 A266299 * A266301 A266302 A266303

Keyword

nonn,tabf,easy

Author

Robert Price, Dec 26 2015

Status

approved