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A271261
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 326", based on the 5-celled von Neumann neighborhood.
1
1, 6, 10, 30, 39, 76, 100, 164, 177, 234, 278, 418, 467, 632, 700, 888, 960, 1216, 1352, 1728, 1853, 2302, 2518, 3094, 3291, 3860, 4148, 4876, 5149, 5890, 6190, 7098, 7511, 8544, 8892, 9984, 10489, 11758, 12194, 13342, 13879, 15340, 15976, 17636, 18244
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=326; 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. A271259.
Sequence in context: A271600 A271134 A272087 * A271412 A272278 A272508
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 02 2016
STATUS
approved