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A267041
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Binary representation of the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 101, 1010, 1100011, 1111100, 11110001111, 111110000, 111111000111111, 11111000000, 1111111100011111111, 1111100000000, 11111111110001111111111, 111110000000000, 111111111111000111111111111, 11111000000000000, 1111111111111100011111111111111
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listen;
history;
text;
internal format)
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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) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>8.
G.f.: (1 +101*x-9091*x^2 +79810*x^3 -8080810*x^4 +100810100*x^5 -10092910100*x^6 -101000000*x^7 +10101000000*x^8) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)).
(End)
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MATHEMATICA
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rule=91; 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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EXTENSIONS
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STATUS
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approved
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