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A266975
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Binary representation of the n-th iteration of the "Rule 78" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 110, 11100, 1101000, 111010000, 11010100000, 1110101000000, 110101010000000, 11101010100000000, 1101010101000000000, 111010101010000000000, 11010101010100000000000, 1110101010101000000000000, 110101010101010000000000000, 11101010101010100000000000000
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refs;
listen;
history;
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internal format)
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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 08 2016 and Apr 18 2019: (Start)
a(n) = 2^(n-2)*5^(n-1)*(9*(-10)^n+2189*10^n-20)/99 for n>0.
a(n) = 10*a(n-1)+10000*a(n-2)-100000*a(n-3) for n>3.
G.f.: (1+100*x-10000*x^3) / ((1-10*x)*(1-100*x)*(1+100*x)).
(End)
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MATHEMATICA
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rule=78; 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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