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A272991 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 569", based on the 5-celled von Neumann neighborhood. 4
1, 4, 17, 28, 61, 93, 133, 149, 213, 297, 353, 413, 497, 577, 685, 665, 781, 1029, 1093, 1245, 1381, 1473, 1701, 1757, 1929, 2189, 2281, 2417, 2633, 2741, 2941, 2965, 3153, 3649, 3757, 4177, 4377, 4553, 4977, 5113, 5377, 5693, 5901, 6145, 6653, 6773, 7081 (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=569; 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: A273610 A272769 A273646 * A273430 A273073 A272330

Adjacent sequences:  A272988 A272989 A272990 * A272992 A272993 A272994

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 12 2016

STATUS

approved

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Last modified November 16 00:11 EST 2018. Contains 317252 sequences. (Running on oeis4.)