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 A273641 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 813", based on the 5-celled von Neumann neighborhood. 1
 7, 13, 23, 25, 48, 36, 52, 36, 103, 73, 76, 52, 172, 76, 108, 44, 240, 128, 100, 68, 312, 160, 116, 132, 244, 188, 160, 88, 460, 148, 144, 152, 388, 284, 196, 132, 524, 276, 292, 220, 332, 372, 260, 276, 496, 328, 84, 356, 512, 464, 240, 88, 808, 384, 364 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Initialized with a single black (ON) cell at stage zero. First negative term is a(95) = -104. Georg Fischer, Feb 15 2019 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 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=813; 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. A258448. Sequence in context: A301691 A163676 A273605 * A214794 A043104 A339112 Adjacent sequences: A273638 A273639 A273640 * A273642 A273643 A273644 KEYWORD sign,easy AUTHOR Robert Price, May 27 2016 STATUS approved

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Last modified August 15 12:13 EDT 2024. Contains 375173 sequences. (Running on oeis4.)