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A272250
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 446", based on the 5-celled von Neumann neighborhood.
1
1, 6, 18, 43, 71, 123, 187, 296, 372, 513, 665, 898, 1090, 1371, 1683, 2076, 2360, 2805, 3261, 3886, 4390, 5079, 5799, 6668, 7352, 8333, 9245, 10414, 11498, 12711, 14091, 15560, 16820, 18453, 20089, 22062, 23786, 25847, 27963, 30372, 32380, 34965, 37385
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=446; 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. A272194.
Sequence in context: A330844 A068293 A334839 * A272700 A191101 A184630
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 23 2016
STATUS
approved