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 A269702 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 243", based on the 5-celled von Neumann neighborhood. 4
 1, 5, 9, 41, 21, 101, 49, 185, 61, 309, 97, 449, 125, 633, 201, 829, 177, 1117, 205, 1445, 181, 1681, 385, 1925, 437, 2337, 465, 2717, 521, 3141, 765, 3465, 729, 4117, 673, 4697, 761, 5117, 1013, 5613, 933, 6337, 1133, 6797, 1345, 7437, 1549, 8189, 1293 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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..128 Robert Price, Diagrams of the first 20 stages. 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=243; 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}]; Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *) CROSSREFS Sequence in context: A304849 A270622 A270673 * A271016 A176967 A110421 Adjacent sequences:  A269699 A269700 A269701 * A269703 A269704 A269705 KEYWORD nonn,easy AUTHOR Robert Price, Mar 28 2016 STATUS approved

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Last modified January 22 07:09 EST 2021. Contains 340360 sequences. (Running on oeis4.)