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A272116
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 430", based on the 5-celled von Neumann neighborhood.
1
1, 6, 14, 35, 59, 96, 140, 225, 321, 422, 538, 687, 855, 1052, 1280, 1621, 2021, 2378, 2798, 3203, 3675, 4128, 4660, 5257, 5953, 6598, 7354, 8143, 9055, 9988, 11080, 12445, 14093, 15474, 17142, 18571, 20291, 21768, 23548, 25169, 27113, 28782, 30786, 32599
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=430; 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. A272115.
Sequence in context: A271283 A272311 A271158 * A268275 A272548 A036387
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 20 2016
STATUS
approved