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A269697
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Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.
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1
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1, 6, 10, 30, 34, 54, 70, 150, 154, 174, 190, 270, 286, 366, 430, 750, 754, 774, 790, 870, 886, 966, 1030, 1350, 1366, 1446, 1510, 1830, 1894, 2214, 2470, 3750, 3754, 3774, 3790, 3870, 3886, 3966, 4030, 4350, 4366, 4446, 4510, 4830, 4894, 5214, 5470, 6750
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OFFSET
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0,2
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COMMENTS
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Initialized with a single black (ON) cell at stage zero.
Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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LINKS
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MATHEMATICA
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rule=6; stages=300;
ca=CellularAutomaton[{rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *)
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
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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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