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A267006
Triangle read by rows giving successive states of cellular automaton generated by "Rule 84" initiated with a single ON (black) cell.
3
1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0
OFFSET
0
COMMENTS
Row n has length 2n+1.
This sequence is also generated by Rules 116, 212 and 244.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
EXAMPLE
The first ten rows:
1
0 1 1
0 0 0 1 1
0 0 0 0 0 1 1
0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
MAPLE
seq(abs( floor(sqrt(n+2)) - 2*floor(sqrt(n+1)) + floor(sqrt(n)) ), n = 0..100); # Peter Bala, Apr 08 2017
MATHEMATICA
rule=84; 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 *)
PROG
(PARI) for(n=0, 100, print1(abs(sqrtint(n + 2) - 2*sqrtint(n + 1) + sqrtint(n)), ", ")) \\ Indranil Ghosh, Apr 08 2017
CROSSREFS
Cf. A266298.
Sequence in context: A275973 A218173 A068426 * A280816 A265246 A138709
KEYWORD
nonn,tabf,easy
AUTHOR
Robert Price, Jan 08 2016
STATUS
approved