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A267351
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Decimal representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 5, 14, 119, 56, 2015, 224, 32639, 896, 523775, 3584, 8386559, 14336, 134209535, 57344, 2147450879, 229376, 34359607295, 917504, 549755289599, 3670016, 8796090925055, 14680064, 140737479966719, 58720256, 2251799780130815, 234881024, 36028796884746239
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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 14 2016 and Apr 19 2019: (Start)
a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>6.
G.f.: (1+5*x-7*x^2+14*x^3-154*x^4-64*x^5+160*x^6) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
(End)
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MATHEMATICA
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rule=123; 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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EXTENSIONS
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STATUS
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approved
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