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A272986 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 566", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 21, 29, 37, 49, 65, 101, 125, 129, 185, 197, 205, 217, 293, 337, 393, 385, 525, 529, 537, 549, 605, 741, 649, 845, 885, 953, 917, 837, 1341, 1149, 1337, 1393, 1353, 1633, 1537, 1717, 1693, 2029, 1837, 2041, 2217, 2297, 2417, 2429, 2569, 2625, 2897 (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=566; 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: A255264 A147407 A186297 * A273642 A169649 A273739

Adjacent sequences:  A272983 A272984 A272985 * A272987 A272988 A272989

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 12 2016

STATUS

approved

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Last modified November 21 11:01 EST 2018. Contains 317447 sequences. (Running on oeis4.)