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A270208
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 121", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 46, 63, 163, 203, 367, 408, 708, 797, 1237, 1313, 1949, 2082, 2882, 3055, 4143, 4336, 5624, 5889, 7489, 7837, 9717, 10090, 12414, 12758, 15407, 15971, 18956, 19520, 23025, 23665, 27618, 28374, 32723, 33439, 38492, 39208, 44705, 45513, 51662, 52642
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=121; 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. A270206.
Sequence in context: A271416 A270179 A268503 * A271463 A272425 A174935
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 13 2016
STATUS
approved