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A273295 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 629", based on the 5-celled von Neumann neighborhood. 4
1, 8, 20, 45, 61, 112, 132, 201, 225, 348, 384, 485, 485, 680, 676, 893, 901, 1153, 1113, 1385, 1305, 1724, 1576, 1993, 1825, 2404, 2240, 2737, 2521, 3208, 2980, 3669, 3317, 4076, 3728, 4693, 4237, 5120, 4660, 5805, 5413, 6352, 5764, 6933, 6261, 7673, 6929 (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=629; 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: A121307 A086169 A273241 * A273266 A273304 A169878

Adjacent sequences:  A273292 A273293 A273294 * A273296 A273297 A273298

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 19 2016

STATUS

approved

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Last modified October 18 04:28 EDT 2019. Contains 328145 sequences. (Running on oeis4.)