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A267293
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Binary representation of the n-th iteration of the "Rule 121" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 1, 11010, 111011, 111011100, 1011101111, 1101101110000, 11111110111111, 11100000111000000, 101111101011111111, 110110001101100000000, 1111111011111111111111, 1110000011100000000000000, 10111110101111111111111111, 11011000110110000000000000000
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OFFSET
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0,3
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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FORMULA
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Conjectures from Colin Barker, Jan 15 2016 and Apr 19 2019: (Start)
a(n) = a(n-2)+100000000*a(n-4)-100000000*a(n-6) for n>12.
G.f.: (1 +x +11009*x^2 +111010*x^3 +11000090*x^4 +910990100*x^5 +90098900*x^6 +9099010000*x^7 -1109990110000*x^8 +979901000000*x^9 -108789011000000*x^10 -989900000000*x^11 +109898900000000*x^12) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +10000*x^2)).
(End)
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MATHEMATICA
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rule=121; 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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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