A267272 Triangle read by rows giving successive states of cellular automaton generated by "Rule 117" initiated with a single ON (black) cell.

1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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
                0 1 1
              1 1 0 0 0
            0 0 1 1 1 1 1
          1 1 0 0 0 0 0 0 0
        0 0 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 1 1 1 1 1 1 1
  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
The full writeup, including leading sequences of 0's and 1's in the rows, gives the following pattern:
00000000000000100000000000000
11111111111110111111111111111
00000000000011000000000000000
11111111111001111111111111111
00000000001100000000000000000
11111111100111111111111111111
00000000110000000000000000000
11111110011111111111111111111
00000011000000000000000000000
11111001111111111111111111111
00001100000000000000000000000
- R. J. Mathar, Aug 07 2025

Mathematica

rule=117; 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: A284677 A191232 A267814 * A181656 A090971 A105594

Adjacent sequences: A267269 A267270 A267271 * A267273 A267274 A267275

Keyword

nonn,tabf,easy

Author

Robert Price, Jan 12 2016

Status

approved