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 A272223 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 441", based on the 5-celled von Neumann neighborhood. 1
 1, 5, 14, 50, 75, 171, 236, 428, 525, 809, 958, 1394, 1575, 2155, 2460, 3272, 3621, 4641, 5022, 6362, 6767, 8347, 8908, 10840, 11473, 13605, 14486, 16998, 17955, 20767, 22036, 25320, 26593, 30365, 31730, 36126, 37483, 42247, 43852, 49216, 51173, 56953, 59050 (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 Robert Price, Table of n, a(n) for n = 0..128 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 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=441; 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 *) Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *) CROSSREFS Cf. A272221. Sequence in context: A075827 A134418 A272147 * A107242 A203164 A063835 Adjacent sequences:  A272220 A272221 A272222 * A272224 A272225 A272226 KEYWORD nonn,easy AUTHOR Robert Price, Apr 22 2016 STATUS approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)