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A272045 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 419", based on the 5-celled von Neumann neighborhood. 4
1, 5, 13, 28, 25, 101, 56, 169, 96, 265, 137, 341, 141, 553, 233, 737, 333, 857, 353, 1057, 429, 1353, 484, 1585, 616, 1841, 693, 2061, 753, 2549, 889, 2917, 1133, 3141, 1137, 3497, 1317, 4017, 1369, 4553, 1661, 4769, 1657, 5277, 1853, 5829, 1897, 6405, 2229 (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=419; 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: A062480 A027024 A296775 * A248860 A185039 A316537

Adjacent sequences:  A272042 A272043 A272044 * A272046 A272047 A272048

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 18 2016

STATUS

approved

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Last modified February 22 23:44 EST 2020. Contains 332157 sequences. (Running on oeis4.)