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 A273456 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 734", based on the 5-celled von Neumann neighborhood. 1
 4, 8, 8, 12, 16, 12, 20, 32, 28, 16, 12, 44, 48, 4, 68, 88, 56, -36, 100, 60, 92, 32, 72, 208, 64, -8, 120, 112, 88, -32, 144, 256, 80, -32, 200, 200, 64, 80, 144, 360, 72, -72, 176, 232, 120, 64, 192, 360, 144, -104, 288, 304, 168, 176, 168, 512, 64, -104 (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=734; 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[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *) CROSSREFS Cf. A273453. Sequence in context: A141719 A098352 A273395 * A299771 A294963 A014198 Adjacent sequences:  A273453 A273454 A273455 * A273457 A273458 A273459 KEYWORD sign,easy AUTHOR Robert Price, May 22 2016 STATUS approved

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)