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A267052
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Decimal representation of the n-th iteration of the "Rule 92" elementary cellular automaton starting with a single ON (black) cell.
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3
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1, 3, 7, 11, 23, 43, 87, 171, 343, 683, 1367, 2731, 5463, 10923, 21847, 43691, 87383, 174763, 349527, 699051, 1398103, 2796203, 5592407, 11184811, 22369623, 44739243, 89478487, 178956971, 357913943, 715827883, 1431655767, 2863311531, 5726623063, 11453246123
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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 10 2016 and Apr 17 2019: (Start)
a(n) = (3+2*(-1)^n+2^(2+n))/3 for n>0.
a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>3.
G.f.: (1+x-4*x^3) / ((1-x)*(1+x)*(1-2*x)).
(End)
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MATHEMATICA
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rule=92; 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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STATUS
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approved
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