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A267213
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Number of OFF (white) cells in the n-th iteration of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
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1
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0, 2, 0, 5, 2, 4, 3, 10, 4, 7, 8, 12, 7, 12, 10, 15, 12, 14, 13, 20, 14, 17, 18, 22, 17, 22, 20, 25, 22, 24, 23, 30, 24, 27, 28, 32, 27, 32, 30, 35, 32, 34, 33, 40, 34, 37, 38, 42, 37, 42, 40, 45, 42, 44, 43, 50, 44, 47, 48, 52, 47, 52, 50, 55, 52, 54, 53
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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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Conjectures from Colin Barker, Jan 13 2016 and Apr 19 2019: (Start)
a(n) = a(n-3)+a(n-4)-a(n-7) for n>7.
G.f.: x*(2+5*x^2+2*x^4-2*x^5+3*x^6) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).
(End)
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MATHEMATICA
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rule=109; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White 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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STATUS
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approved
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