

A270177


Number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 113", based on the 5celled von Neumann neighborhood.


4



1, 4, 9, 32, 17, 88, 37, 184, 44, 297, 92, 429, 112, 629, 100, 845, 140, 1009, 224, 1324, 225, 1632, 244, 1897, 380, 2221, 328, 2597, 464, 3021, 532, 3445, 560, 3837, 648, 4417, 792, 4845, 756, 5485, 940, 5953, 1044, 6717, 1020, 7169, 1292, 7777, 1468, 8561
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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

Robert Price, Table of n, a(n) for n = 0..128
Robert Price, Diagrams of the first 20 stages.
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
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=113; 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+1n, k1+n]], {j, k+1n, k1+n}], {n, 1, k}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)


CROSSREFS

Sequence in context: A271305 A270160 A271414 * A268277 A270206 A271461
Adjacent sequences: A270174 A270175 A270176 * A270178 A270179 A270180


KEYWORD

nonn,easy


AUTHOR

Robert Price, Mar 12 2016


STATUS

approved



