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A270317 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 149", based on the 5-celled von Neumann neighborhood. 4
1, 8, 4, 44, 5, 116, 12, 209, 12, 348, 25, 492, 37, 696, 57, 892, 60, 1165, 88, 1436, 89, 1756, 112, 2089, 152, 2465, 136, 2888, 225, 3264, 236, 3749, 240, 4293, 256, 4757, 316, 5373, 300, 5933, 340, 6548, 505, 7116, 529, 7788, 525, 8456, 641, 9276, 577 (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=149; 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: A270729 A270465 A270980 * A270329 A270626 A270677

Adjacent sequences:  A270314 A270315 A270316 * A270318 A270319 A270320

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 15 2016

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)