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A281284
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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 350", based on the 5-celled von Neumann neighborhood.
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4
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1, 3, 3, 11, 27, 11, 59, 203, 123, 267, 1467, 4043, 123, 4363, 21947, 62667, 14203, 102667, 316859, 939211, 227195, 1642763, 5076411, 15013067, 3635067, 26284299, 81229243, 240194763, 58161019, 420548875, 1299674555, 3843101899, 930576251, 6728782091
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OFFSET
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0,2
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COMMENTS
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Initialized with a single black (ON) cell at stage zero.
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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LINKS
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FORMULA
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a(n) = 17*a(n-4) - 16*a(n-8) for n > 23.
G.f.: (49152*x^23 + 40960*x^22 - 32768*x^21 - 12288*x^20 - 61440*x^19 - 32768*x^18 + 32768*x^17 + 14080*x^16 - 2816*x^15 - 2048*x^14 - 1536*x^12 + 768*x^11 + 512*x^10 + 128*x^9 - 320*x^8 + 16*x^7 + 8*x^6 - 40*x^5 + 10*x^4 + 11*x^3 + 3*x^2 + 3*x + 1)/(16*x^8 - 17*x^4 + 1). (End)
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MATHEMATICA
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CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 350; 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}]
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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