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A267157
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Decimal representation of the middle column of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 2, 4, 9, 19, 39, 79, 159, 319, 639, 1278, 2557, 5114, 10229, 20458, 40917, 81834, 163669, 327338, 654677, 1309354, 2618709, 5237418, 10474837, 20949674, 41899349, 83798698, 167597397, 335194794, 670389589, 1340779178, 2681558357, 5363116714, 10726233429
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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 11 2016 and Apr 19 2019: (Start)
a(n) = (-(-1)^n+959*2^(n-7)-3)/6 for n>7.
a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4.
G.f.: (1-x^2+x^3+x^4-x^10) / ((1-x)*(1+x)*(1-2*x)).
(End)
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MATHEMATICA
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rule=107; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}] (* Binary Representation of Middle Column *)
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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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