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A270722
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 201", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 42, 59, 139, 167, 300, 364, 605, 677, 1025, 1134, 1666, 1803, 2459, 2671, 3536, 3740, 4789, 5085, 6434, 6738, 8295, 8727, 10508, 11004, 13089, 13721, 16142, 16862, 19567, 20311, 23416, 24328, 27832, 28681, 32713, 33873, 38222, 39350, 44254, 45487
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=201; 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. A270720.
Sequence in context: A198086 A272018 A272091 * A272282 A270893 A272316
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 22 2016
STATUS
approved