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A272311
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood.
1
1, 6, 14, 35, 55, 87, 135, 200, 256, 340, 424, 536, 672, 868, 1084, 1381, 1625, 1925, 2233, 2501, 2857, 3253, 3721, 4293, 4817, 5361, 5977, 6721, 7517, 8417, 9377, 10522, 11534, 12618, 13670, 14790, 15978, 17246, 18722, 20314, 21982, 23602, 25386, 27162
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=462; 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. A246330.
Sequence in context: A271089 A271695 A271283 * A271158 A272116 A268275
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 25 2016
STATUS
approved