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A271018
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 251", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 56, 77, 178, 227, 412, 473, 782, 879, 1328, 1461, 2074, 2299, 3060, 3297, 4310, 4583, 5864, 6173, 7746, 8163, 10004, 10457, 12654, 13215, 15752, 16421, 19306, 20267, 23332, 24305, 27878, 28887, 32984, 34029, 38674, 39827, 44996, 46185, 51966, 53263
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=251; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
CROSSREFS
Cf. A271016.
Sequence in context: A270624 A270675 A271002 * A145638 A361567 A067665
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 28 2016
STATUS
approved