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A273602 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 805", based on the 5-celled von Neumann neighborhood. 4
1, 8, 21, 44, 69, 113, 145, 200, 249, 328, 397, 489, 537, 652, 741, 840, 913, 1088, 1205, 1380, 1477, 1632, 1737, 1900, 2017, 2248, 2405, 2624, 2741, 2968, 3157, 3368, 3501, 3788, 4089, 4312, 4505, 4776, 4965, 5260, 5393, 5760, 6101, 6456, 6653, 6940, 7225 (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=805; 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: A180672 A152117 A075629 * A258448 A138179 A067334

Adjacent sequences:  A273599 A273600 A273601 * A273603 A273604 A273605

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 26 2016

STATUS

approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)