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A271012 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 249", based on the 5-celled von Neumann neighborhood. 4
1, 4, 13, 40, 25, 88, 81, 176, 61, 316, 124, 424, 217, 560, 297, 828, 224, 1064, 377, 1248, 485, 1568, 656, 1888, 637, 2184, 905, 2580, 996, 2921, 1344, 3253, 1152, 3852, 1292, 4181, 1620, 4617, 1708, 5325, 1920, 5720, 2316, 6389, 2284, 6901, 2940, 7361 (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=249; 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: A121192 A133409 A000746 * A272581 A191132 A119915

Adjacent sequences:  A271009 A271010 A271011 * A271013 A271014 A271015

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 28 2016

STATUS

approved

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Last modified November 20 12:37 EST 2018. Contains 317402 sequences. (Running on oeis4.)