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A266629
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Total number of OFF (white) cells after n iterations of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
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1
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0, 2, 3, 8, 12, 16, 21, 28, 38, 44, 56, 67, 81, 90, 104, 117, 136, 148, 169, 186, 212, 225, 247, 271, 300, 315, 350, 375, 400, 429, 460, 489, 526, 556, 592, 619, 665, 688, 740, 766, 815, 851, 898, 931, 992, 1021, 1078, 1116, 1175, 1213, 1271, 1315, 1381
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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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MATHEMATICA
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rule=45; 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,easy
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AUTHOR
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STATUS
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approved
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