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A271067
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 262", based on the 5-celled von Neumann neighborhood.
1
1, 6, 10, 30, 39, 72, 85, 150, 170, 262, 299, 400, 445, 578, 647, 844, 929, 1142, 1231, 1464, 1557, 1866, 1963, 2356, 2469, 2942, 3075, 3592, 3697, 4126, 4310, 5094, 5314, 6054, 6306, 7102, 7366, 8190, 8454, 9478, 9822, 10862, 11202, 12270, 12602, 13662
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=262; 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. A271065.
Sequence in context: A025129 A093559 A269697 * A271600 A271134 A272087
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 29 2016
STATUS
approved