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A271604
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 393", based on the 5-celled von Neumann neighborhood.
1
1, 5, 10, 38, 47, 131, 160, 296, 313, 593, 638, 1014, 1063, 1591, 1708, 2312, 2417, 3289, 3438, 4514, 4683, 6043, 6232, 7836, 8069, 9965, 10226, 12430, 12823, 15207, 15652, 18248, 18737, 21745, 22310, 25738, 26275, 30315, 30904, 35396, 35997, 41093, 41738
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=393; 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. A271602.
Sequence in context: A174933 A270219 A270276 * A365690 A277816 A359021
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 10 2016
STATUS
approved