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A267598 Triangle read by rows giving successive states of cellular automaton generated by "Rule 177" initiated with a single ON (black) cell. 2
1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
Row n has length 2n+1.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
a(n) = (1 - (-1)^(n + floor(sqrt(n + 2))))/2 (conjecture). - Velin Yanev, Nov 15 2016
EXAMPLE
The first ten rows:
1
0 0 1
0 1 0 0 1
0 1 0 1 0 0 1
0 1 0 1 0 1 0 0 1
0 1 0 1 0 1 0 1 0 0 1
0 1 0 1 0 1 0 1 0 1 0 0 1
0 1 0 1 0 1 0 1 0 1 0 1 0 0 1
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1
MATHEMATICA
rule=177; 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: A232990 A285076 A338353 * A194681 A359764 A065043
KEYWORD
nonn,tabf,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved

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Last modified April 20 22:14 EDT 2024. Contains 371848 sequences. (Running on oeis4.)