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A273328
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 646", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 28, 37, 66, 83, 144, 161, 238, 271, 396, 441, 602, 671, 928, 989, 1270, 1355, 1708, 1805, 2194, 2315, 2800, 2921, 3454, 3623, 4300, 4505, 5290, 5567, 6640, 6885, 8006, 8299, 9564, 9869, 11170, 11499, 12896, 13225, 14670, 15047, 16636, 17049, 18746
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=646; 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. A273326.
Sequence in context: A273705 A165819 A087737 * A273423 A273760 A273837
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 20 2016
STATUS
approved