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A270467
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 173", based on the 5-celled von Neumann neighborhood.
1
1, 9, 13, 53, 70, 182, 202, 382, 443, 767, 808, 1244, 1360, 2004, 2077, 2897, 3090, 4174, 4294, 5602, 5882, 7510, 7658, 9590, 9950, 12230, 12466, 15086, 15598, 18638, 18914, 22366, 22982, 26970, 27398, 31598, 32550, 37386, 37866, 43434, 44346, 50458, 51062
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=173; 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. A270465.
Sequence in context: A270948 A270284 A270731 * A270982 A323797 A270319
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 17 2016
STATUS
approved