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 A285774 Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 84", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 2, 0, 4, 0, 40, 0, 16, 0, 160, 0, 1088, 0, 10880, 0, 256, 0, 2560, 0, 17408, 0, 174080, 0, 1052672, 0, 10526720, 0, 71581696, 0, 715816960, 0, 65536, 0, 655360, 0, 4456448, 0, 44564480, 0, 269484032, 0, 2694840320, 0, 18324914176, 0, 183249141760, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Initialized with a single black (ON) cell at stage zero. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Robert Price, Table of n, a(n) for n = 0..126 Robert Price, Diagrams of first 20 stages N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Wolfram Research, Wolfram Atlas of Simple Programs MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 84; stages = 128; rule = IntegerDigits[code, 2, 10]; g = 2 * stages + 1; (* Maximum size of grid *) a = PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *) ca = a; ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; PrependTo[ca, a]; (* Trim full grid to reflect growth by one cell at each stage *) k = (Length[ca[]] + 1)/2; ca = Table[Table[Part[ca[[n]] [[j]], Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}]; Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] CROSSREFS Cf. A285771, A285772, A285773. Sequence in context: A007420 A019219 A019139 * A262589 A019215 A326799 Adjacent sequences:  A285771 A285772 A285773 * A285775 A285776 A285777 KEYWORD nonn,easy AUTHOR Robert Price, Apr 25 2017 STATUS approved

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Last modified August 16 22:14 EDT 2022. Contains 356169 sequences. (Running on oeis4.)