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A272784 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 533", based on the 5-celled von Neumann neighborhood. 1
1, 9, 29, 66, 130, 214, 355, 504, 748, 997, 1358, 1734, 2218, 2759, 3432, 4116, 4976, 5853, 6926, 8038, 9338, 10687, 12248, 13888, 15684, 17653, 19774, 22034, 24478, 27071, 29876, 32868, 36012, 39385, 42946, 46786, 50702, 54987, 59360, 64168, 68976, 74233 (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=533; 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. A272782.

Sequence in context: A272732 A272740 A162263 * A272807 A316602 A331390

Adjacent sequences:  A272781 A272782 A272783 * A272785 A272786 A272787

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 06 2016

STATUS

approved

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Last modified June 6 10:48 EDT 2020. Contains 334844 sequences. (Running on oeis4.)