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A272746 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 529", based on the 5-celled von Neumann neighborhood. 4
1, 4, 13, 28, 49, 77, 96, 149, 180, 257, 256, 373, 388, 513, 476, 709, 692, 857, 828, 1129, 1032, 1301, 1224, 1605, 1584, 1789, 1812, 2149, 2132, 2445, 2368, 2861, 2684, 3121, 3100, 3461, 3544, 3785, 3848, 4341, 4284, 4817, 4772, 5237, 5292, 5697, 5784, 6085 (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=529; 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: A307272 A056107 A155433 * A273557 A272790 A273564

Adjacent sequences:  A272743 A272744 A272745 * A272747 A272748 A272749

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 05 2016

STATUS

approved

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Last modified April 19 01:29 EDT 2019. Contains 322237 sequences. (Running on oeis4.)