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 A272146 Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 433", based on the 5-celled von Neumann neighborhood. 0
 1, 4, 36, 180, 796, 3096, 13032, 52596, 209744, 843956, 3377876, 13516812, 54090596, 216400164, 865705764, 3463093152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 Table of n, a(n) for n=0..15. 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 Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=433; 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]]]+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}]; on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *) Part[on, 2^Range[0, Log[2, stages]]] (* Extract relevant terms *) CROSSREFS Cf. A272145. Sequence in context: A272557 A370660 A276295 * A372218 A034569 A270084 Adjacent sequences: A272143 A272144 A272145 * A272147 A272148 A272149 KEYWORD nonn,more AUTHOR Robert Price, Apr 21 2016 EXTENSIONS a(8)-a(15) from Lars Blomberg, Jul 02 2016 STATUS approved

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Last modified July 18 15:13 EDT 2024. Contains 374388 sequences. (Running on oeis4.)