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A272585
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Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 507", based on the 5-celled von Neumann neighborhood.
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4
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1, 5, 13, 40, 29, 100, 69, 200, 85, 324, 133, 480, 181, 644, 309, 872, 325, 1124, 373, 1408, 421, 1700, 565, 2048, 613, 2404, 757, 2792, 901, 3140, 1301, 3624, 1317, 4132, 1365, 4672, 1413, 5220, 1557, 5824, 1605, 6436, 1749, 7080, 1893, 7684, 2325, 8416
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OFFSET
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0,2
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COMMENTS
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Initialized with a single black (ON) cell at stage zero.
Similar to A272581 (Rule 505). Only a(1) appears to be different.
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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LINKS
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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
Index entries for sequences related to cellular automata
Index to 2D 5-Neighbor Cellular Automata
Index to Elementary Cellular Automata
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MATHEMATICA
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CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=507; 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 *)
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CROSSREFS
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Sequence in context: A077919 A295913 A272225 * A026069 A054856 A261057
Adjacent sequences: A272582 A272583 A272584 * A272586 A272587 A272588
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KEYWORD
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nonn,easy
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AUTHOR
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Robert Price, May 03 2016
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STATUS
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approved
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