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A272449
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 475", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 47, 76, 160, 221, 393, 478, 762, 903, 1291, 1484, 2060, 2341, 3045, 3398, 4402, 4775, 6019, 6512, 7956, 8601, 10337, 11154, 13202, 14143, 16515, 17528, 20216, 21473, 24617, 26078, 29754, 31007, 35115, 36740, 41288, 43005, 48073, 50126, 55634, 57855
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=475; 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. A272447.
Sequence in context: A271456 A271537 A271891 * A270455 A318414 A106272
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 29 2016
STATUS
approved