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 A272454 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 478", based on the 5-celled von Neumann neighborhood. 1
 4, 7, 9, 11, 12, 29, 3, 33, -5, 81, -29, 81, -21, 149, -113, 145, -29, 173, -149, 257, -101, 253, -197, 213, -5, 185, -121, 241, -81, 317, -245, 433, -173, 293, -81, 205, 55, 241, -181, 377, -205, 381, -121, 297, -45, 281, 75, 169, 79, 245, -221, 577, -181 (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=478; 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. A272451. Sequence in context: A053169 A007656 A159619 * A207017 A174724 A267873 Adjacent sequences:  A272451 A272452 A272453 * A272455 A272456 A272457 KEYWORD sign,easy AUTHOR Robert Price, Apr 29 2016 STATUS approved

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Last modified June 16 21:20 EDT 2019. Contains 324155 sequences. (Running on oeis4.)