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A263244
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Binary representation of the n-th iteration of the "Rule 155" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 101, 10011, 1011111, 100111111, 10111111111, 1001111111111, 101111111111111, 10011111111111111, 1011111111111111111, 100111111111111111111, 10111111111111111111111, 1001111111111111111111111, 101111111111111111111111111, 10011111111111111111111111111
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OFFSET
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0,2
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LINKS
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FORMULA
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Conjectures from Colin Barker, Jan 20 2016 and Apr 17 2019: (Start)
a(n) = a(n-1)+10000*a(n-2)-10000*a(n-3) for n>3.
G.f.: (1+100*x-90*x^2+1100*x^3) / ((1-x)*(1-100*x)*(1+100*x)).
(End)
Conjecture: a(n) = floor(91*100^((n-1)/2)*10^n/9) for odd n; a(n) = floor(901*100^(n/2 - 1)*10^n/9) for even n. - Karl V. Keller, Jr., May 01 2022
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MATHEMATICA
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rule=155; 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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