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A273121 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 593", based on the 5-celled von Neumann neighborhood. 1
1, 5, 22, 47, 107, 172, 309, 445, 669, 890, 1235, 1563, 2039, 2508, 3149, 3813, 4609, 5458, 6459, 7527, 8747, 10032, 11525, 13049, 14785, 16582, 18627, 20723, 23059, 25488, 28149, 30973, 34021, 37214, 40570, 44206, 48131, 52084, 56492, 60888, 65753, 70590 (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=593; 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. A273119.

Sequence in context: A184724 A082005 A273024 * A099078 A272836 A273575

Adjacent sequences:  A273118 A273119 A273120 * A273122 A273123 A273124

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 15 2016

STATUS

approved

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Last modified July 4 23:17 EDT 2022. Contains 355086 sequences. (Running on oeis4.)