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 A273249 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 617", based on the 5-celled von Neumann neighborhood. 1
 3, 17, 8, 43, 16, 64, 0, 112, 24, 112, 16, 160, 8, 184, -72, 288, 16, 264, 16, 240, 24, 328, -72, 424, -56, 432, -104, 504, -192, 608, -408, 768, -128, 664, -144, 616, -168, 800, -120, 700, -136, 724, -184, 888, -256, 868, -576, 1292, -352, 1004, -512, 1280 (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=617; 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. A273246. Sequence in context: A093844 A273211 A273273 * A273303 A033467 A096475 Adjacent sequences: A273246 A273247 A273248 * A273250 A273251 A273252 KEYWORD sign,easy AUTHOR Robert Price, May 18 2016 STATUS approved

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Last modified January 29 11:06 EST 2023. Contains 359922 sequences. (Running on oeis4.)