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A267576
Triangle read by rows giving successive states of cellular automaton generated by "Rule 167" initiated with a single ON (black) cell.
8
1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1
OFFSET
0
COMMENTS
Row n has length 2n+1.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
EXAMPLE
The first ten rows:
1
1 1 0
1 1 0 1 0
1 1 0 1 1 1 0
1 1 0 1 0 1 0 1 0
1 1 0 1 1 1 1 1 1 1 0
1 1 0 1 0 1 1 1 1 1 0 1 0
1 1 0 1 1 1 0 1 1 1 0 1 1 1 0
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
The full writeup of the rule has an infinite sequence of leading and trailing 1's from row 2 on:
00000000000000100000000000000
11111111111111101111111111111
11111111111111010111111111111
11111111111110111011111111111
11111111111101010101111111111
11111111111011111110111111111
11111111110101111101011111111
11111111101110111011101111111
11111111010101010101010111111
11111110111111111111111011111
11111101011111111111110101111
- R. J. Mathar, Aug 07 2025
MATHEMATICA
rule=167; 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: A080909 A087755 A050072 * A156707 A131309 A267208
KEYWORD
nonn,tabf,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved