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A271454
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 371", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 32, 21, 96, 41, 169, 40, 309, 108, 389, 68, 649, 140, 805, 156, 1089, 244, 1229, 269, 1588, 261, 1908, 417, 2260, 437, 2612, 497, 3084, 493, 3444, 737, 3924, 617, 4464, 713, 4996, 881, 5460, 977, 5980, 1173, 6700, 1093, 7344, 1293, 7828, 1373, 8604
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=371; 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: A266206 A271397 A264099 * A265916 A271889 A272447
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 08 2016
STATUS
approved