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 A273211 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 609", based on the 5-celled von Neumann neighborhood. 1
 3, 17, 8, 43, 12, 57, 27, 80, 41, 51, 37, 100, 48, 72, 32, 179, 100, 173, 72, 80, 123, 113, 28, 195, 181, 143, 133, 175, 197, 155, -35, 311, 268, 284, 100, 296, 120, 156, 144, 244, 332, 176, 172, 316, 372, 109, 15, 493, 523, 148, 97, 407, 420, 176, 348, 276 (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=609; 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. A273208. Sequence in context: A140446 A124689 A093844 * A273273 A273249 A273303 Adjacent sequences:  A273208 A273209 A273210 * A273212 A273213 A273214 KEYWORD sign,easy AUTHOR Robert Price, May 17 2016 STATUS approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)