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 A273779 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 926", based on the 5-celled von Neumann neighborhood. 1
 4, 8, 8, 16, 8, 32, 8, 32, 8, 64, 8, 32, 40, 96, -24, 64, 8, 128, 8, 32, 104, 160, -88, 128, 8, 128, 136, 32, 104, 288, -216, 128, 8, 256, 8, 32, 232, 288, -216, 256, 8, 128, 392, 32, 104, 544, -472, 128, 136, 384, -120, 160, 360, 160, 168, 384, -120, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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..127 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=926; 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 *) CROSSREFS Cf. A273750. Sequence in context: A083744 A255992 A273572 * A114027 A005877 A144174 Adjacent sequences:  A273776 A273777 A273778 * A273780 A273781 A273782 KEYWORD sign,easy AUTHOR Robert Price, May 30 2016 STATUS approved

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Last modified December 14 09:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)