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A272805 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 541", based on the 5-celled von Neumann neighborhood. 4
1, 8, 20, 37, 64, 84, 141, 149, 244, 249, 369, 376, 504, 525, 696, 660, 893, 881, 1092, 1117, 1321, 1352, 1653, 1577, 1912, 1861, 2273, 2176, 2568, 2473, 3049, 2828, 3332, 3241, 3821, 3568, 4228, 4033, 4749, 4500, 5156, 4965, 5757, 5448, 6284, 5925, 6921 (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=541; 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: A272730 A272738 A272782 * A073607 A086062 A006416

Adjacent sequences:  A272802 A272803 A272804 * A272806 A272807 A272808

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 06 2016

STATUS

approved

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Last modified June 17 17:12 EDT 2019. Contains 324196 sequences. (Running on oeis4.)