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A272330 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 601", based on the 5-celled von Neumann neighborhood. 4
1, 4, 17, 29, 61, 73, 132, 148, 244, 224, 357, 349, 505, 461, 705, 645, 956, 816, 1144, 996, 1413, 1205, 1749, 1477, 2057, 1717, 2389, 2097, 2764, 2364, 3225, 2781, 3669, 3029, 4116, 3408, 4605, 3833, 5129, 4329, 5717, 4725, 6257, 5241, 6792, 5708, 7529 (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
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
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=601; 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: A272991 A273430 A273073 * A163736 A249582 A127547
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 17 2016
STATUS
approved

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)