A263804 Triangle read by rows giving successive states of cellular automaton generated by "Rule 157" initiated with a single ON (black) cell.

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

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

Mathematica

rule=157; 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: A070829 A118175 A179762 * A120526 A086694 A357518

Adjacent sequences: A263801 A263802 A263803 * A263805 A263806 A263807

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 17 2016

Status

approved