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A272313
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 465", based on the 5-celled von Neumann neighborhood.
3
1, 4, 9, 28, 25, 84, 49, 140, 89, 260, 113, 380, 161, 532, 233, 620, 345, 868, 369, 1116, 417, 1396, 489, 1612, 609, 1956, 681, 2236, 825, 2548, 1041, 2604, 1369, 3108, 1393, 3612, 1441, 4148, 1513, 4620, 1633, 5220, 1705, 5756, 1849, 6324, 2065, 6636, 2401
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.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=465; 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: A272280 A087726 A270891 * A239668 A101973 A244968
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 25 2016
STATUS
approved