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A266721
Decimal representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
4
1, 2, 5, 11, 22, 45, 90, 181, 362, 725, 1450, 2901, 5802, 11605, 23210, 46421, 92842, 185685, 371370, 742741, 1485482, 2970965, 5941930, 11883861, 23767722, 47535445, 95070890, 190141781, 380283562, 760567125, 1521134250, 3042268501, 6084537002, 12169074005
OFFSET
0,2
FORMULA
From Colin Barker, Jan 05 2016 and Apr 17 2019: (Start)
a(n) = (-2*(-1)^n+17*2^n-6)/12 for n>1.
a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4.
G.f.: (1+x^3-x^4) / ((1-x)*(1+x)*(1-2*x)). (End)
a(n) = floor(17*2^n/12). - Karl V. Keller, Jr., Oct 17 2021
MATHEMATICA
rule=59; 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 *)
PROG
(Python) print([17*2**n//12 for n in range(50)]) # Karl V. Keller, Jr., Oct 18 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 03 2016
STATUS
approved