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A267882
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Total number of ON (black) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 1, 4, 10, 19, 30, 43, 58, 75, 94, 115, 138, 163, 190, 219, 250, 283, 318, 355, 394, 435, 478, 523, 570, 619, 670, 723, 778, 835, 894, 955, 1018, 1083, 1150, 1219, 1290, 1363, 1438, 1515, 1594, 1675, 1758, 1843, 1930, 2019, 2110, 2203, 2298, 2395, 2494
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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, Jan 22 2016 and Apr 20 2019: (Start)
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
G.f.: (1-2*x+4*x^2-x^5) / (1-x)^3.
(End)
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MATHEMATICA
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rule=233; 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[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through 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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