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A266790
Binary representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
2
1, 11, 111, 1110, 11101, 111010, 1110101, 11101010, 111010100, 1110101001, 11101010011, 111010100111, 1110101001110, 11101010011101, 111010100111010, 1110101001110101, 11101010011101010, 111010100111010101, 1110101001110101010, 11101010011101010101
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)
a(n) = (-9*(-1)^n+1098999991099*2^(n-9)*5^(n-10)-11)/198 for n>9.
G.f.: (1+x-x^3-x^8+x^9+x^10-x^12) / ((1-x)*(1+x)*(1-10*x)).
(End)
MATHEMATICA
rule=61; 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 03 2016
STATUS
approved