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A272841 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 547", based on the 5-celled von Neumann neighborhood. 1
4, 12, 12, 32, 28, 32, 28, 64, 60, 64, 60, 80, 60, 64, 60, 128, 124, 128, 124, 144, 124, 128, 124, 176, 156, 152, 140, 144, 84, 96, 124, 256, 252, 256, 252, 272, 252, 256, 252, 304, 284, 280, 268, 272, 212, 224, 252, 368, 348, 344, 332, 336, 276, 280, 300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Initialized with a single black (ON) cell at stage zero.

The first negative term is a(123) = -88. - Georg Fischer, Feb 15 2019

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=547; 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. A272838.

Sequence in context: A294628 A323188 A284126 * A272942 A272923 A161411

Adjacent sequences:  A272838 A272839 A272840 * A272842 A272843 A272844

KEYWORD

sign,easy,changed

AUTHOR

Robert Price, May 07 2016

STATUS

approved

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Last modified February 22 09:55 EST 2019. Contains 320390 sequences. (Running on oeis4.)