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A271202
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 313", based on the 5-celled von Neumann neighborhood.
1
1, 5, 10, 42, 55, 143, 164, 332, 369, 653, 730, 1174, 1247, 1867, 1976, 2780, 2961, 3969, 4142, 5470, 5691, 7279, 7568, 9516, 9797, 12089, 12486, 15142, 15523, 18559, 19040, 22592, 23101, 27085, 27734, 32174, 32895, 37923, 38700, 44256, 45053, 51197, 52062
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=313; 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. A271200.
Sequence in context: A269874 A270077 A271150 * A186031 A305246 A316546
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 01 2016
STATUS
approved