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A267526
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Binary representation of the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 10, 101, 1011, 1010111, 10101111, 10101011111, 101010111111, 101010101111111, 1010101011111111, 1010101010111111111, 10101010101111111111, 10101010101011111111111, 101010101010111111111111, 101010101010101111111111111, 1010101010101011111111111111
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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) = 11*a(n-1) + 9990*a(n-2) - 110000*a(n-3) + 100000*a(n-4) for n > 5.
G.f.: (1 - x - 9999*x^2 + 10000*x^3 + 990000*x^4 - 1000000*x^5) / ((1-x)*(1-10*x)*(1-100*x)*(1+100*x)). - [corrected by Karl V. Keller, Jr., Sep 18 2021]
(End)
Conjecture: a(n) = 10^n*(100^floor(n/2) - 1)/99 + (10^(n-1) - 1)/9 for n > 1. - Karl V. Keller, Jr., Sep 22 2021
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MATHEMATICA
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rule=141; 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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