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A272543 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 493", based on the 5-celled von Neumann neighborhood. 4
1, 8, 5, 44, 17, 112, 29, 204, 61, 336, 73, 492, 109, 672, 157, 876, 229, 1136, 241, 1420, 277, 1728, 329, 2044, 429, 2432, 477, 2812, 573, 3264, 633, 3652, 861, 4168, 873, 4708, 909, 5272, 961, 5844, 1061, 6488, 1113, 7108, 1237, 7800, 1353, 8388, 1645 (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

Robert Price, Diagrams of the first 20 stages

MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=493; 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: A271689 A272111 A272291 * A272007 A296437 A038283

Adjacent sequences:  A272540 A272541 A272542 * A272544 A272545 A272546

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 02 2016

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)