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A272045
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 419", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 28, 25, 101, 56, 169, 96, 265, 137, 341, 141, 553, 233, 737, 333, 857, 353, 1057, 429, 1353, 484, 1585, 616, 1841, 693, 2061, 753, 2549, 889, 2917, 1133, 3141, 1137, 3497, 1317, 4017, 1369, 4553, 1661, 4769, 1657, 5277, 1853, 5829, 1897, 6405, 2229
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=419; 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: A062480 A027024 A296775 * A248860 A185039 A344521
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 18 2016
STATUS
approved