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A267538
Binary representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.
3
1, 11, 110, 1100, 11001, 110011, 1100111, 11001111, 110011111, 1100111111, 11001111111, 110011111111, 1100111111111, 11001111111111, 110011111111111, 1100111111111111, 11001111111111111, 110011111111111111, 1100111111111111111, 11001111111111111111
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 17 2016 and Apr 20 2019: (Start)
a(n) = 11*a(n-1)-10*a(n-2) for n > 4. [n range correction by Karl V. Keller, Jr., Apr 23 2022]
G.f.: (1-x^2+x^4) / ((1-x)*(1-10*x)).
(End)
Conjecture: a(n) = floor(9901*10^n/9000). - Karl V. Keller, Jr., Apr 24 2022
MATHEMATICA
rule=143; 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]], {k, 1, rows}] (* Binary Representation of Middle Column *)
CROSSREFS
Sequence in context: A278664 A259661 A265699 * A278819 A274474 A272609
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 16 2016
STATUS
approved