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A258448 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. 4
1, 8, 21, 44, 69, 117, 153, 205, 241, 344, 417, 493, 545, 717, 793, 901, 945, 1185, 1313, 1413, 1481, 1793, 1953, 2069, 2201, 2445, 2633, 2793, 2881, 3341, 3489, 3633, 3785, 4173, 4457, 4653, 4785, 5309, 5585, 5877, 6097, 6429, 6801, 7061, 7337, 7833, 8161 (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=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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A152117 A075629 A273602 * A344599 A138179 A067334
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved

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Last modified April 12 19:05 EDT 2024. Contains 371636 sequences. (Running on oeis4.)