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A266206 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 315", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 32, 13, 104, 25, 192, 53, 324, 65, 425, 121, 609, 120, 845, 101, 1136, 105, 1365, 232, 1621, 212, 2045, 248, 2297, 380, 2669, 533, 3032, 545, 3533, 573, 3968, 621, 4556, 725, 4940, 805, 5468, 961, 6084, 1101, 6608, 1105, 7360, 1205, 8048, 1269, 8652 (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=315; 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: A271129 A271152 A271164 * A271397 A264099 A271454

Adjacent sequences:  A266203 A266204 A266205 * A266207 A266208 A266209

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 02 2016

STATUS

approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)