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A273486 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 758", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 21, 33, 45, 61, 85, 129, 157, 189, 221, 281, 309, 357, 413, 489, 549, 613, 677, 769, 829, 909, 989, 1097, 1173, 1269, 1349, 1473, 1533, 1645, 1765, 1905, 2029, 2157, 2285, 2441, 2565, 2709, 2853, 3025, 3165, 3325, 3469, 3657, 3781, 3957, 4133, 4337 (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

Robert Price, Diagrams of the first 20 stages

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=758; 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}];

Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

CROSSREFS

Sequence in context: A319384 A211427 A273410 * A146867 A068481 A146827

Adjacent sequences:  A273483 A273484 A273485 * A273487 A273488 A273489

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 23 2016

STATUS

approved

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Last modified July 6 23:56 EDT 2020. Contains 335484 sequences. (Running on oeis4.)