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A270636 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood. 1
1, 5, 14, 46, 79, 171, 236, 412, 465, 781, 894, 1326, 1515, 2063, 2347, 3148, 3448, 4476, 4896, 6168, 6644, 8132, 8804, 10644, 11320, 13500, 14340, 16828, 17804, 20632, 21844, 25164, 26424, 30140, 31564, 35836, 37284, 41940, 43720, 48976, 50908, 56608, 58820 (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=185; 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. A270634.
Sequence in context: A272425 A174935 A270620 * A077335 A176640 A126729
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 20 2016
STATUS
approved

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Last modified April 20 15:29 EDT 2024. Contains 371844 sequences. (Running on oeis4.)