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A270020
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 51", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 48, 57, 166, 179, 392, 405, 738, 767, 1260, 1293, 1978, 2047, 2924, 3001, 4134, 4227, 5648, 5733, 7458, 7583, 9652, 9789, 12246, 12387, 15224, 15389, 18682, 18863, 22620, 22829, 27038, 27271, 32004, 32293, 37578, 37887, 43724, 44033, 50514, 50919
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=51; 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. A270018.
Sequence in context: A270327 A270932 A269816 * A269878 A292120 A099437
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 08 2016
STATUS
approved