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A267855
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Decimal representation of the n-th iteration of the "Rule 230" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 6, 20, 120, 368, 1888, 5952, 30592, 96000, 488960, 1537024, 7829504, 24604672, 125263872, 393691136, 2004320256, 6299254784, 32068993024, 100788338688, 513105461248, 1612616564736, 8209685282816, 25801869230080, 131354989690880, 412829958012928
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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 17 2019: (Start)
a(n) = 16*a(n-2)+16*a(n-4)-256*a(n-6) for n>5.
G.f.: (1+6*x+4*x^2+24*x^3+32*x^4-128*x^5) / ((1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)*(1+4*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]], 2], {k, 1, rows}] (* Decimal 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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