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A273499
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 771", based on the 5-celled von Neumann neighborhood.
3
1, 5, 17, 33, 65, 89, 137, 161, 257, 297, 377, 401, 561, 601, 713, 705, 1025, 1097, 1241, 1265, 1553, 1593, 1769, 1697, 2273, 2345, 2553, 2513, 2993, 2969, 3209, 2945, 4097, 4233, 4505, 4529, 5073, 5113, 5417, 5217, 6305, 6377, 6713, 6545, 7409, 7257, 7625
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=771; 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: A128354 A078654 A083364 * A297520 A026394 A004538
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved