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A272275 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 453", based on the 5-celled von Neumann neighborhood. 1
1, 9, 14, 54, 71, 175, 204, 392, 441, 741, 802, 1262, 1355, 1947, 2096, 2904, 3021, 4085, 4282, 5550, 5787, 7363, 7592, 9472, 9757, 11945, 12242, 14778, 15187, 18139, 18580, 21928, 22465, 26305, 26790, 31058, 31735, 36515, 37248, 42428, 43293, 49193, 49986 (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=453; 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. A272273.

Sequence in context: A027009 A239038 A271596 * A272051 A272504 A197955

Adjacent sequences:  A272272 A272273 A272274 * A272276 A272277 A272278

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 24 2016

STATUS

approved

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Last modified January 18 00:56 EST 2021. Contains 340249 sequences. (Running on oeis4.)