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A273449
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 726", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 21, 21, 53, 53, 73, 85, 141, 141, 161, 185, 257, 261, 229, 297, 445, 421, 437, 497, 597, 597, 557, 657, 965, 925, 961, 1029, 1217, 1237, 1189, 1349, 1665, 1741, 1729, 1829, 1849, 2025, 1957, 2117, 2569, 2637, 2585, 2829, 2769, 2993, 2861, 3149, 3505
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=726; 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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A272786 A273150 A273388 * A297362 A376288 A175364
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 22 2016
STATUS
approved