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A267854
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Binary representation of the n-th iteration of the "Rule 230" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 110, 10100, 1111000, 101110000, 11101100000, 1011101000000, 111011110000000, 10111011100000000, 1110111011000000000, 101110111010000000000, 11101110111100000000000, 1011101110111000000000000, 111011101110110000000000000, 10111011101110100000000000000
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OFFSET
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0,2
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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FORMULA
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Conjectures from Colin Barker, Jan 21 2016 and Apr 20 2019: (Start)
a(n) = 10000*a(n-2)+10000*a(n-4)-100000000*a(n-6) for n>5.
G.f.: (1+110*x+100*x^2+11000*x^3+100000*x^4-10000000*x^5) / ((1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)*(1+100*x^2)).
(End)
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MATHEMATICA
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rule=230; 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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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