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A273425 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 718", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 17, 21, 29, 37, 69, 81, 89, 105, 129, 149, 189, 221, 285, 301, 285, 289, 329, 381, 413, 469, 477, 501, 541, 593, 697, 745, 849, 905, 1061, 1213, 1173, 1133, 1149, 1225, 1345, 1385, 1469, 1521, 1565, 1733, 1853, 2013, 2133, 2253, 2589, 2705, 2653 (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=718; 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: A315118 A190848 A273330 * A273762 A273851 A097538
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 22 2016
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)