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A267003
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Decimal representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 5, 8, 111, 64, 1919, 512, 31743, 4096, 516095, 32768, 8323071, 262144, 133693439, 2097152, 2143289343, 16777216, 34326183935, 134217728, 549487378431, 1073741824, 8793945538559, 8589934592, 140720308486143, 68719476736, 2251662374731775, 549755813888
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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 19 2019: (Start)
a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>5.
G.f.: (1+2*x)*(1+3*x-23*x^2+32*x^3-48*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).
(End)
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MATHEMATICA
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rule=83; 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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