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A270982
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 237", based on the 5-celled von Neumann neighborhood.
1
1, 9, 13, 53, 70, 182, 202, 386, 447, 775, 820, 1288, 1384, 2060, 2189, 3009, 3145, 4294, 4422, 5783, 6019, 7776, 7996, 9937, 10337, 12665, 12941, 15714, 16150, 19367, 19959, 23507, 24127, 28220, 28900, 33501, 34333, 39565, 40397, 45973, 47090, 53426, 54323
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=237; 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. A270980.
Sequence in context: A270284 A270731 A270467 * A323797 A270319 A270331
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 27 2016
STATUS
approved