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

Author

Hans Havermann, May 26 2002

Keywords

• nonn
• tabf

Comments

Row n has length 2n+1.

Examples

			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
		

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

Crossrefs

See A071051 for number of ON states.

The right half is the triangle A127872.

Cf. A036987 (central column).

Programs

Mathematica

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

Extensions

Corrected by Hans Havermann, Jan 07 2012