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A266327
Binary representation of the n-th iteration of the "Rule 20" elementary cellular automaton starting with a single ON (black) cell.
1
1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11
OFFSET
0,2
COMMENTS
Rules 52, 148 and 180 also generate this sequence.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Dec 28 2015 and Apr 18 2019: (Start)
a(n) = 6-5*(-1)^n.
a(n) = a(n-2) for n>1.
G.f.: (1+11*x) / ((1-x)*(1+x)).
(End)
MATHEMATICA
rule=20; 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
Cf. A266326.
Sequence in context: A231920 A230891 A063431 * A274216 A280524 A317845
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 27 2015
STATUS
approved