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A270452
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 161", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 38, 67, 131, 180, 296, 397, 613, 702, 1010, 1191, 1647, 1784, 2388, 2681, 3441, 3674, 4654, 5067, 6227, 6572, 8016, 8557, 10213, 10702, 12674, 13391, 15631, 16272, 18868, 19777, 22689, 23490, 26806, 27939, 31587, 32596, 36720, 38085, 42565, 43798
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=161; 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. A270450.
Sequence in context: A045553 A270687 A272254 * A270463 A183898 A225865
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 17 2016
STATUS
approved