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A269918 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 822", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 25, 37, 49, 57, 105, 117, 153, 161, 229, 253, 297, 289, 417, 397, 545, 585, 661, 709, 745, 737, 949, 909, 1073, 1033, 1309, 1285, 1425, 1289, 1657, 1509, 1881, 1985, 2269, 2237, 2449, 2537, 2725, 2693, 2953, 2929, 3245, 3277, 3409, 3241, 3805, 3445 (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=822; 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: A273561 A273746 A234277 * A273827 A024825 A147074

Adjacent sequences:  A269915 A269916 A269917 * A269919 A269920 A269921

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 27 2016

STATUS

approved

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Last modified February 27 13:18 EST 2020. Contains 332306 sequences. (Running on oeis4.)