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A267811
Binary representation of the n-th iteration of the "Rule 217" elementary cellular automaton starting with a single ON (black) cell.
1
1, 1, 11011, 1110111, 111101111, 11111011111, 1111110111111, 111111101111111, 11111111011111111, 1111111110111111111, 111111111101111111111, 11111111111011111111111, 1111111111110111111111111, 111111111111101111111111111, 11111111111111011111111111111
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) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>4.
G.f.: (1-110*x+12010*x^2-112000*x^3+100000*x^4) / ((1-x)*(1-10*x)*(1-100*x)).
(End)
MATHEMATICA
rule=217; 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. A267810.
Sequence in context: A267293 A300557 A181319 * A267934 A218598 A096930
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 20 2016
STATUS
approved