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A270450
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 161", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 24, 29, 64, 49, 116, 101, 216, 89, 308, 181, 456, 137, 604, 293, 760, 233, 980, 413, 1160, 345, 1444, 541, 1656, 489, 1972, 717, 2240, 641, 2596, 909, 2912, 801, 3316, 1133, 3648, 1009, 4124, 1365, 4480, 1233, 5020, 1605, 5408, 1489, 5980, 1893
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=161; 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: A329879 A320059 A373002 * A270461 A046422 A288099
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 17 2016
STATUS
approved