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A267153
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Binary representation of the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 100, 1011, 1101110, 1110111, 11110111010, 111011011, 111111011111110, 11100000111, 1111111101011111010, 1101100011011, 11111111111111011111110, 11100000111, 111111111111111101011111010, 1101100011011, 1111111111111111111111011111110, 11100000111
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OFFSET
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0,2
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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 11 2016 and Apr 19 2019: (Start)
a(n) = 10000*a(n-2)+a(n-4)-10000*a(n-6) for n>12.
G.f.: (1 +100*x -8989*x^2 +101110*x^3 -8999890*x^4 +99010910*x^5 -10990090000*x^6 +9900910000*x^7 -1099001110000*x^8 +989801000000*x^9 -109887911000000*x^10 +100990000000000*x^11 -11009890000000000*x^12) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +x^2)).
(End)
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MATHEMATICA
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rule=107; 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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EXTENSIONS
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STATUS
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approved
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