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A271809
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 403", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 43, 60, 156, 201, 357, 406, 699, 807, 1192, 1288, 1885, 2089, 2730, 2955, 3928, 4224, 5321, 5650, 7043, 7508, 9116, 9557, 11450, 12083, 14211, 14876, 17480, 18205, 21118, 21874, 25275, 26192, 29844, 30949, 35142, 36391, 41027, 42308, 47408, 48889
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=403; 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. A271807.
Sequence in context: A370933 A230165 A271687 * A272289 A272320 A137806
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 14 2016
STATUS
approved