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A266256
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Number of ON (black) cells in the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
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3
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1, 1, 2, 5, 2, 9, 2, 13, 2, 17, 2, 21, 2, 25, 2, 29, 2, 33, 2, 37, 2, 41, 2, 45, 2, 49, 2, 53, 2, 57, 2, 61, 2, 65, 2, 69, 2, 73, 2, 77, 2, 81, 2, 85, 2, 89, 2, 93, 2, 97, 2, 101, 2, 105, 2, 109, 2, 113, 2, 117, 2, 121, 2, 125, 2, 129, 2, 133, 2, 137, 2, 141
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OFFSET
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0,3
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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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Conjectures from Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)
a(n) = (-2*((-1)^n-1)*n+3*(-1)^n+1)/2 for n>0.
a(n) = 2*a(n-2)-a(n-4) for n>4.
G.f.: (1+x+3*x^3-x^4) / ((1-x)^2*(1+x)^2).
(End)
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MATHEMATICA
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rule=11; 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[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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