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A270687
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 193", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 38, 59, 131, 176, 288, 381, 605, 722, 1042, 1215, 1679, 1884, 2412, 2705, 3553, 3778, 4878, 5023, 6511, 6872, 8268, 8861, 10605, 11142, 13178, 13859, 16211, 16911, 19212, 20284, 23253, 24045, 27634, 28250, 32343, 33387, 37588, 38848, 43601, 44781
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=193; 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. A270685.
Sequence in context: A072130 A196976 A045553 * A272254 A270452 A270463
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 21 2016
STATUS
approved