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A273557 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 785", based on the 5-celled von Neumann neighborhood. 4
1, 4, 13, 28, 49, 77, 104, 141, 180, 241, 268, 353, 392, 485, 544, 629, 700, 825, 884, 1033, 1104, 1261, 1352, 1501, 1604, 1777, 1868, 2049, 2184, 2341, 2464, 2645, 2780, 3033, 3156, 3433, 3568, 3853, 4008, 4285, 4452, 4753, 4908, 5217, 5416, 5701, 5888 (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=785; 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: A056107 A155433 A272746 * A272790 A273564 A155392

Adjacent sequences:  A273554 A273555 A273556 * A273558 A273559 A273560

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 25 2016

STATUS

approved

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Last modified August 13 22:57 EDT 2020. Contains 336473 sequences. (Running on oeis4.)