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A266460
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Binary representation of the n-th iteration of the "Rule 27" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 101, 10, 1111011, 100, 11111110111, 1000, 111111111101111, 10000, 1111111111111011111, 100000, 11111111111111110111111, 1000000, 111111111111111111101111111, 10000000, 1111111111111111111111011111111, 100000000, 11111111111111111111111110111111111
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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, Dec 31 2015 and Apr 16 2019: (Start)
a(n) = 10011*a(n-2)-110010*a(n-4)+100000*a(n-6) for n>5.
G.f.: (1+101*x-10001*x^2+99900*x^3+10000*x^4-110000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)).
(End)
Conjecture: a(n) = (10*(100^n - 9*10^floor(n/2)) - 1)/9 for odd n; a(n) = 10^(n/2) for even n. - Karl V. Keller, Jr., Sep 29 2021
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MATHEMATICA
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rule=27; 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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