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A270317 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 149", based on the 5-celled von Neumann neighborhood. 4
1, 8, 4, 44, 5, 116, 12, 209, 12, 348, 25, 492, 37, 696, 57, 892, 60, 1165, 88, 1436, 89, 1756, 112, 2089, 152, 2465, 136, 2888, 225, 3264, 236, 3749, 240, 4293, 256, 4757, 316, 5373, 300, 5933, 340, 6548, 505, 7116, 529, 7788, 525, 8456, 641, 9276, 577 (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
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
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=149; 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: A270980 A373109 A360354 * A270329 A270626 A270677
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 15 2016
STATUS
approved

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Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)