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A272113
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 429", based on the 5-celled von Neumann neighborhood.
1
1, 9, 14, 58, 75, 183, 216, 424, 481, 809, 894, 1394, 1491, 2139, 2288, 3208, 3369, 4469, 4726, 6194, 6371, 8079, 8368, 10488, 10809, 13169, 13670, 16578, 16963, 20163, 20752, 24516, 25133, 29209, 29994, 34806, 35499, 40687, 41680, 47604, 48561, 54901, 56146
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=429; 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. A272111.
Sequence in context: A272155 A272566 A271691 * A272293 A272545 A272009
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 20 2016
STATUS
approved