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A272539 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 491", based on the 5-celled von Neumann neighborhood. 4
1, 5, 13, 32, 41, 76, 77, 164, 137, 240, 173, 428, 249, 520, 317, 800, 405, 892, 525, 1248, 589, 1408, 733, 1824, 837, 2012, 1025, 2484, 1141, 2700, 1329, 3276, 1465, 3512, 1681, 4172, 1825, 4424, 2089, 5164, 2225, 5456, 2525, 6264, 2673, 6592, 2997, 7464 (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=491; 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: A066688 A046789 A271902 * A066184 A231799 A146924

Adjacent sequences:  A272536 A272537 A272538 * A272540 A272541 A272542

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 02 2016

STATUS

approved

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Last modified June 26 13:53 EDT 2022. Contains 354883 sequences. (Running on oeis4.)