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A272219 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 438", based on the 5-celled von Neumann neighborhood. 1
1, 6, 14, 34, 66, 106, 142, 242, 355, 467, 607, 799, 1023, 1267, 1523, 1875, 2255, 2695, 3167, 3695, 4235, 4787, 5375, 6075, 6791, 7667, 8579, 9695, 10743, 11795, 12871, 14319, 15752, 17312, 18812, 20665, 22501, 24425, 26233, 28365, 30549, 32945, 35169 (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

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=438; 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}];

on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)

CROSSREFS

Cf. A272217.

Sequence in context: A270024 A271198 A270632 * A271089 A271695 A271283

Adjacent sequences:  A272216 A272217 A272218 * A272220 A272221 A272222

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 22 2016

STATUS

approved

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Last modified April 6 20:32 EDT 2020. Contains 333286 sequences. (Running on oeis4.)