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A267036
Decimal representation of the n-th iteration of the "Rule 85" elementary cellular automaton starting with a single ON (black) cell.
2
1, 3, 16, 63, 256, 1023, 4096, 16383, 65536, 262143, 1048576, 4194303, 16777216, 67108863, 268435456, 1073741823, 4294967296, 17179869183, 68719476736, 274877906943, 1099511627776, 4398046511103, 17592186044416, 70368744177663, 281474976710656
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 11 2016 and Apr 19 2019: (Start)
a(n) = ((-1)^n-1)/2+4^n.
a(n) = 4*a(n-1)+a(n-2)-4*a(n-3) for n>2.
G.f.: (1-x+3*x^2) / ((1-x)*(1+x)*(1-4*x)).
(End)
MATHEMATICA
rule=85; 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 *)
CROSSREFS
Sequence in context: A370305 A355645 A323941 * A037451 A247363 A007143
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 09 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022
STATUS
approved