A071035 Triangle read by rows giving successive states of cellular automaton generated by "Rule 126".

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

Offset

0,1

Comments

Row n has length 2n+1.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

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 to Elementary Cellular Automata

Index entries for sequences related to cellular automata

Example

Triangle begins:
                           1,
                        1, 1, 1,
                     1, 1, 0, 1, 1,
                  1, 1, 1, 1, 1, 1, 1,
               1, 1, 0, 0, 0, 0, 0, 1, 1,
            1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1,
         1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1,
      1, 1, 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, 1, 1,
1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,
... - N. J. A. Sloane, Aug 24 2014

Mathematica

A071035list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&, CellularAutomaton[126, {{1}, 0}, rowmax]]; A071035list[10] (* Generates 11 rows *) (* Paolo Xausa, Jul 18 2023 *)

Crossrefs

See A071051 for number of ON states.

The right half is the triangle A127872.

Cf. A036987 (central column).

Sequence in context: A089509 A157972 A124897 * A138345 A014590 A015171

Adjacent sequences: A071032 A071033 A071034 * A071036 A071037 A071038

Keyword

nonn,tabf

Author

Hans Havermann, May 26 2002

Extensions

Corrected by Hans Havermann, Jan 07 2012

Status

approved