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A267688
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Binary representation of the n-th iteration of the "Rule 199" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 110, 11100, 1111010, 111110100, 11111101010, 1111111010100, 111111110101010, 11111111101010100, 1111111111010101010, 111111111110101010100, 11111111111101010101010, 1111111111111010101010100, 111111111111110101010101010, 11111111111111101010101010100
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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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a(n) = 110*a(n-1) - 999*a(n-2) - 110*a(n-3) + 1000*a(n-4) for n > 4.
G.f.: (1 - x^2 + 10*x^3 - 1000*x^4) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).
(End)
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MATHEMATICA
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rule=199; 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
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AUTHOR
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STATUS
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approved
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