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A273758 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 902", based on the 5-celled von Neumann neighborhood. 4
1, 5, 5, 17, 9, 29, 17, 61, 21, 65, 53, 105, 65, 137, 81, 233, 109, 217, 129, 337, 173, 313, 257, 429, 317, 497, 341, 645, 393, 701, 469, 777, 697, 733, 705, 1005, 689, 845, 841, 1165, 929, 1233, 1109, 1213, 1101, 1241, 1325, 1521, 1657, 1693, 1553, 1885 (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=902; 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: A300784 A273326 A273421 * A273835 A246333 A079317

Adjacent sequences:  A273755 A273756 A273757 * A273759 A273760 A273761

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 29 2016

STATUS

approved

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Last modified May 28 13:20 EDT 2020. Contains 334683 sequences. (Running on oeis4.)