A266754 Triangle read by rows giving successive states of cellular automaton generated by "Rule 165" initiated with a single ON (black) cell.

1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 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..10000

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

Mathematica

rule=165; 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: A135022 A286726 A189209 * A071982 A266588 A157749

Adjacent sequences: A266751 A266752 A266753 * A266755 A266756 A266757

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 17 2016

Status

approved