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A266718
Decimal representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
3
1, 5, 6, 123, 12, 2039, 24, 32751, 48, 524255, 96, 8388543, 192, 134217599, 384, 2147483391, 768, 34359737855, 1536, 549755812863, 3072, 8796093020159, 6144, 140737488351231, 12288, 2251799813677055, 24576, 36028797018947583, 49152, 576460752303390719, 98304
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)
a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>6.
G.f.: (1-2*x)*(1+7*x+x^2+30*x^3+8*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).
(End)
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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
CROSSREFS
Sequence in context: A041139 A065354 A078984 * A041257 A337465 A041411
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 03 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022
STATUS
approved