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A267876
Binary representation of the n-th iteration of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
1
1, 0, 10101, 1110111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111, 1111111111111111111111111, 111111111111111111111111111, 11111111111111111111111111111
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)
a(n) = 101*a(n-1)-100*a(n-2) for n>3.
G.f.: (1-101*x+10201*x^2+89910*x^3-100000*x^5) / ((1-x)*(1-100*x)).
(End)
MATHEMATICA
rule=233; 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. A267868.
Sequence in context: A258189 A114385 A267680 * A353110 A144863 A300558
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 21 2016
STATUS
approved