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A271463
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 377", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 46, 63, 167, 196, 376, 437, 749, 822, 1282, 1403, 2055, 2192, 3052, 3221, 4297, 4558, 5866, 6159, 7807, 8148, 10128, 10477, 12777, 13290, 15894, 16455, 19543, 20108, 23700, 24361, 28257, 29130, 33542, 34351, 39295, 40200, 45748, 46713, 52825, 53926
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=377; 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. A271461.
Sequence in context: A270179 A268503 A270208 * A272425 A174935 A270620
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 08 2016
STATUS
approved