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A271454 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 371", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 32, 21, 96, 41, 169, 40, 309, 108, 389, 68, 649, 140, 805, 156, 1089, 244, 1229, 269, 1588, 261, 1908, 417, 2260, 437, 2612, 497, 3084, 493, 3444, 737, 3924, 617, 4464, 713, 4996, 881, 5460, 977, 5980, 1173, 6700, 1093, 7344, 1293, 7828, 1373, 8604 (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=371; 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: A266206 A271397 A264099 * A265916 A271889 A272447

Adjacent sequences:  A271451 A271452 A271453 * A271455 A271456 A271457

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 08 2016

STATUS

approved

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Last modified February 17 23:47 EST 2018. Contains 299297 sequences. (Running on oeis4.)