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A267829 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 483", based on the 5-celled von Neumann neighborhood. 1
1, 6, 19, 47, 84, 169, 245, 398, 503, 755, 916, 1277, 1486, 2002, 2295, 2980, 3320, 4197, 4653, 5706, 6222, 7651, 8335, 9976, 10736, 12717, 13553, 15690, 16706, 19347, 20531, 23512, 24812, 28221, 29725, 33498, 35086, 39423, 41419, 46208, 48144, 53325, 55609 (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=483; 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. A248860.

Sequence in context: A298741 A070893 A272047 * A027963 A034199 A272752

Adjacent sequences:  A267826 A267827 A267828 * A267830 A267831 A267832

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 01 2016

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)