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A272792 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 537", based on the 5-celled von Neumann neighborhood. 1
1, 5, 18, 46, 95, 176, 264, 437, 630, 883, 1131, 1528, 1936, 2469, 2981, 3722, 4471, 5368, 6225, 7377, 8553, 9878, 11167, 12888, 14437, 16397, 18222, 20419, 22639, 25212, 27528, 30521, 33457, 36750, 39798, 43579, 47235, 51487, 55456, 60189, 64626, 69783 (list; graph; refs; listen; history; text; internal format)
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.
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=537; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
CROSSREFS
Cf. A272790.
Sequence in context: A081435 A272748 A273559 * A273566 A217866 A256539
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 06 2016
STATUS
approved

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Last modified May 22 17:21 EDT 2024. Contains 372758 sequences. (Running on oeis4.)