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A266617
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Total number of OFF (white) cells after n iterations of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
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1
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0, 3, 6, 10, 18, 21, 32, 36, 52, 55, 74, 78, 102, 105, 132, 136, 168, 171, 206, 210, 250, 253, 296, 300, 348, 351, 402, 406, 462, 465, 524, 528, 592, 595, 662, 666, 738, 741, 816, 820, 900, 903, 986, 990, 1078, 1081, 1172, 1176, 1272, 1275, 1374, 1378, 1482
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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 02 2016 and Apr 18 2019: (Start)
a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>6.
G.f.: x*(3+3*x+x^2+5*x^3-4*x^4) / ((1-x)^3*(1+x)^2*(1+x^2)).
(End)
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MATHEMATICA
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rule=41; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)
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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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