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A270221
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 131", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 33, 13, 93, 25, 161, 53, 285, 65, 417, 93, 581, 129, 705, 229, 957, 241, 1217, 269, 1509, 305, 1761, 397, 2117, 433, 2433, 517, 2781, 625, 2945, 965, 3453, 977, 3969, 1005, 4517, 1041, 5025, 1133, 5637, 1169, 6209, 1253, 6813, 1361, 7233, 1677, 7973
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=131; 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: A265798 A259264 A259265 * A270689 A270278 A270725
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 13 2016
STATUS
approved