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A266680
Binary representation of the middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell.
3
1, 11, 110, 1101, 11011, 110111, 1101111, 11011111, 110111111, 1101111111, 11011111111, 110111111111, 1101111111111, 11011111111111, 110111111111111, 1101111111111111, 11011111111111111, 110111111111111111, 1101111111111111111, 11011111111111111111
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 19 2016 and Apr 18 2019: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 3.
G.f.: (1-x^2+x^3) / ((1-x)*(1-10*x)).
(End)
MATHEMATICA
rule=175; 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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved