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 A270637 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood. 1
 3, 5, 23, 1, 59, -27, 111, -123, 263, -203, 319, -243, 359, -264, 517, -501, 728, -608, 852, -796, 1012, -816, 1168, -1164, 1504, -1340, 1648, -1512, 1852, -1616, 2108, -2060, 2456, -2292, 2848, -2824, 3208, -2876, 3476, -3324, 3768, -3488, 4072, -3852, 4308 (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 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=185; 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. A270634. Sequence in context: A212260 A178377 A270621 * A064187 A112686 A318443 Adjacent sequences: A270634 A270635 A270636 * A270638 A270639 A270640 KEYWORD sign,easy AUTHOR Robert Price, Mar 20 2016 STATUS approved

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Last modified April 16 03:20 EDT 2024. Contains 371696 sequences. (Running on oeis4.)