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 A272010 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 413", based on the 5-celled von Neumann neighborhood. 1
 7, -3, 43, -43, 115, -115, 219, -219, 355, -355, 523, -523, 723, -723, 955, -955, 1219, -1219, 1515, -1515, 1843, -1843, 2203, -2203, 2595, -2595, 3019, -3019, 3475, -3475, 3963, -3963, 4483, -4483, 5035, -5035, 5619, -5619, 6235, -6235, 6883, -6883, 7563 (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 Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata FORMULA Conjecture: a(n) = A269909(n), n>0. - R. J. Mathar, Apr 19 2016 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=413; 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. A272007. Sequence in context: A272156 A271815 A194778 * A145758 A038269 A176328 Adjacent sequences: A272007 A272008 A272009 * A272011 A272012 A272013 KEYWORD sign,easy AUTHOR Robert Price, Apr 17 2016 STATUS approved

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Last modified July 19 05:20 EDT 2024. Contains 374388 sequences. (Running on oeis4.)