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A282387 Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood. 5
1, 3, 6, 15, 24, 60, 102, 255, 384, 960, 1632, 4080, 6168, 15420, 26214, 65535, 98304, 245760, 417792, 1044480, 1579008, 3947520, 6710784, 16776960, 25166208, 62915520, 106956384, 267390960, 404232216, 1010580540, 1717986918, 4294967295, 6442450944 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
The first 23 terms of A062878 are the same as this sequence, but I cannot prove nor disprove that these two sequences are the same.
Agrees with A062878 for at least 1000 terms. - Sean A. Irvine, Apr 14 2023
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
MATHEMATICA
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 462; 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[1, i]], 2], {i, 1, stages - 1}]
CROSSREFS
Sequence in context: A282008 A281212 A062878 * A227960 A282484 A286207
KEYWORD
nonn,easy
AUTHOR
Robert Price, Feb 13 2017
STATUS
approved

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Last modified September 23 19:42 EDT 2023. Contains 365554 sequences. (Running on oeis4.)