A267015 Triangle read by rows giving successive states of cellular automaton generated by "Rule 91" initiated with a single ON (black) cell.

1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 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..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
                1 0 1
              0 1 0 1 0
            1 1 0 0 0 1 1
          0 0 1 1 1 1 1 0 0
        1 1 1 1 0 0 0 1 1 1 1
      0 0 0 0 1 1 1 1 1 0 0 0 0
    1 1 1 1 1 1 0 0 0 1 1 1 1 1 1
  0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1
Including leading and trailing 0's and 1's, the rows start to repeat periodically:
00000000000000100000000000000
11111111111111011111111111111
00000000000001010000000000000
11111111111110001111111111111
00000000000011111000000000000
11111111111110001111111111111
00000000000011111000000000000
11111111111110001111111111111
00000000000011111000000000000
11111111111110001111111111111
00000000000011111000000000000
11111111111110001111111111111
00000000000011111000000000000
11111111111110001111111111111
- R. J. Mathar, Aug 07 2025

Mathematica

rule=91; 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: A117569 A135528 A163805 * A078387 A189292 A331168

Adjacent sequences: A267012 A267013 A267014 * A267016 A267017 A267018

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 09 2016

Status

approved