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A266983
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Binary representation of the n-th iteration of the "Rule 81" elementary cellular automaton starting with a single ON (black) cell.
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3
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1, 1, 11000, 11111, 110000000, 111111111, 1100000000000, 1111111111111, 11000000000000000, 11111111111111111, 110000000000000000000, 111111111111111111111, 1100000000000000000000000, 1111111111111111111111111, 11000000000000000000000000000
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OFFSET
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0,3
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COMMENTS
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Rule 113 also generates this sequence.
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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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Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata
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FORMULA
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Conjectures from Colin Barker, Jan 08 2016 and Apr 17 2019: (Start)
a(n) = (49*(-100)^n + 5*(-1)^n + 2^(2*n+1)*25^(n+1)-5)/90 for n > 0.
a(n) = 10001*a(n-2) - 10000*a(n-4) for n > 4.
G.f.: (1 + x + 999*x^2 + 1110*x^3 - 1000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
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MATHEMATICA
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rule=81; 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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Cf. A266982, A266984.
Sequence in context: A252039 A252033 A352751 * A227865 A267777 A034712
Adjacent sequences: A266980 A266981 A266982 * A266984 A266985 A266986
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KEYWORD
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nonn,easy
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AUTHOR
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Robert Price, Jan 07 2016
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STATUS
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approved
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