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A272512 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 489", based on the 5-celled von Neumann neighborhood. 1
1, 5, 18, 50, 83, 183, 248, 408, 505, 805, 950, 1326, 1503, 2083, 2340, 3052, 3397, 4385, 4818, 5930, 6395, 7855, 8456, 10144, 10889, 12989, 13886, 16198, 17095, 19867, 20948, 23996, 25277, 28889, 30370, 34290, 35795, 40295, 42112, 46960, 48953, 54533, 56742 (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=489; 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. A272510.

Sequence in context: A344311 A176145 A270978 * A257055 A036893 A332953

Adjacent sequences:  A272509 A272510 A272511 * A272513 A272514 A272515

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 01 2016

STATUS

approved

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Last modified January 22 12:12 EST 2022. Contains 350481 sequences. (Running on oeis4.)