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A271891
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 411", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 47, 72, 165, 213, 378, 455, 751, 844, 1285, 1441, 2018, 2263, 2983, 3256, 4233, 4545, 5746, 6115, 7603, 8088, 9809, 10434, 12458, 13143, 15447, 16260, 19053, 20069, 23138, 24306, 27839, 28923, 32824, 34132, 38609, 40170, 45086, 46707, 52079, 53880
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=411; 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. A271889.
Sequence in context: A268154 A271456 A271537 * A272449 A270455 A318414
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 16 2016
STATUS
approved