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A273246 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 617", based on the 5-celled von Neumann neighborhood. 4
1, 4, 21, 29, 72, 88, 152, 152, 264, 288, 400, 416, 576, 584, 768, 696, 984, 1000, 1264, 1280, 1520, 1544, 1872, 1800, 2224, 2168, 2600, 2496, 3000, 2808, 3416, 3008, 3776, 3648, 4312, 4168, 4784, 4616, 5416, 5296, 5996, 5860, 6584, 6400, 7288, 7032, 7900 (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

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

MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=617; 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: A316513 A273208 A273270 * A273299 A306285 A273699

Adjacent sequences:  A273243 A273244 A273245 * A273247 A273248 A273249

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 18 2016

STATUS

approved

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Last modified March 26 14:48 EDT 2019. Contains 321497 sequences. (Running on oeis4.)