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A272155
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 437", based on the 5-celled von Neumann neighborhood.
1
1, 9, 14, 58, 67, 179, 200, 420, 445, 789, 830, 1322, 1379, 2091, 2144, 3044, 3149, 4325, 4402, 5846, 5995, 7775, 7940, 10048, 10241, 12717, 12962, 15846, 16155, 19467, 19828, 23604, 24005, 28293, 28650, 33490, 33907, 39299, 39772, 45756, 46269, 52877, 53438
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=437; 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. A272153.
Sequence in context: A197955 A271814 A272418 * A272566 A271691 A272113
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 21 2016
STATUS
approved