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A272989
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 566", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 36, 65, 102, 151, 216, 317, 442, 571, 756, 953, 1158, 1375, 1668, 2005, 2398, 2783, 3308, 3837, 4374, 4923, 5528, 6269, 6918, 7763, 8648, 9601, 10518, 11355, 12696, 13845, 15182, 16575, 17928, 19561, 21098, 22815, 24508, 26537, 28374, 30415, 32632
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=566; 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. A272986.
Sequence in context: A272928 A269567 A253098 * A273644 A273797 A273741
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 12 2016
STATUS
approved