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A273911
Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 614", based on the 5-celled von Neumann neighborhood.
1
1, 3, 5, 11, 17, 55, 69, 219, 257, 775, 1301, 2923, 4113, 12407, 20805, 46811, 65537, 196615, 327701, 721003, 1114385, 3606391, 4527173, 14380507, 16777473, 50333447, 83891477, 184576875, 285282321, 923234423, 1158959429, 3681400539, 4294967297, 12884901895
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=614; 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}];
Table[FromDigits[Part[ca[[i]][[i]], Range[i, 2*i-1]], 2], {i, 1, stages-1}]
CROSSREFS
Cf. A273910.
Sequence in context: A167466 A284144 A283913 * A284242 A284306 A283399
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jun 03 2016
STATUS
approved