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A271695
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 398", based on the 5-celled von Neumann neighborhood.
1
1, 6, 14, 35, 55, 83, 119, 195, 271, 335, 423, 539, 667, 819, 975, 1271, 1579, 1775, 2051, 2327, 2627, 3003, 3327, 3779, 4251, 4663, 5191, 5799, 6415, 7155, 7935, 8939, 10011, 10851, 11855, 12719, 13671, 14743, 15695, 16823, 18007, 19203, 20527, 21951, 23219
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=398; 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. A271693.
Sequence in context: A270632 A272219 A271089 * A271283 A272311 A271158
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 12 2016
STATUS
approved