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A267044
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Binary representation of the middle column of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 10, 100, 1000, 10001, 100010, 1000101, 10001010, 100010101, 1000101010, 10001010101, 100010101010, 1000101010101, 10001010101010, 100010101010101, 1000101010101010, 10001010101010101, 100010101010101010, 1000101010101010101, 10001010101010101010
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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) = (-550+450*(-1)^n+9901*10^n)/9900 for n>1.
a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>4. [Typo corrected by Karl V. Keller, Jr., Mar 16 2022]
G.f.: (1-x^2+x^4) / ((1-x)*(1+x)*(1-10*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 *) 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 *)
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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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