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A267002
Binary representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.
2
1, 101, 1000, 1101111, 1000000, 11101111111, 1000000000, 111101111111111, 1000000000000, 1111101111111111111, 1000000000000000, 11111101111111111111111, 1000000000000000000, 111111101111111111111111111, 1000000000000000000000, 1111111101111111111111111111111
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 08 2016 and Apr 19 2019: (Start)
a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.
G.f.: (1+101*x-10001*x^2-9990*x^3+10000*x^4-1100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
(End)
MATHEMATICA
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]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
Sequence in context: A167842 A244369 A200733 * A242138 A171764 A164842
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 08 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