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A273559 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 785", based on the 5-celled von Neumann neighborhood. 1
1, 5, 18, 46, 95, 172, 276, 417, 597, 838, 1106, 1459, 1851, 2336, 2880, 3509, 4209, 5034, 5918, 6951, 8055, 9316, 10668, 12169, 13773, 15550, 17418, 19467, 21651, 23992, 26456, 29101, 31881, 34914, 38070, 41503, 45071, 48924, 52932, 57217, 61669, 66422 (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=785; 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. A273557.
Sequence in context: A340974 A081435 A272748 * A272792 A273566 A217866
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 25 2016
STATUS
approved

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Last modified May 26 04:31 EDT 2024. Contains 372807 sequences. (Running on oeis4.)