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A272942 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 563", based on the 5-celled von Neumann neighborhood. 1
4, 12, 12, 32, 28, 32, 40, 56, 52, 80, 64, 64, 96, 56, 72, 116, 112, 168, 128, 116, 112, 156, 164, 124, 180, 152, 128, 188, 136, 68, 128, 268, 312, 200, 224, 272, 232, 264, 304, 156, 208, 284, 344, 296, 184, 208, 252, 300, 276, 364, 280, 380, 324, 396, 352 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..127

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=563; 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}];

on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

CROSSREFS

Cf. A272939.

Sequence in context: A323188 A284126 A272841 * A272923 A161411 A261695

Adjacent sequences:  A272939 A272940 A272941 * A272943 A272944 A272945

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 11 2016

STATUS

approved

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Last modified February 21 18:45 EST 2019. Contains 320376 sequences. (Running on oeis4.)