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A273113
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 589", based on the 5-celled von Neumann neighborhood.
1
1, 9, 29, 70, 131, 224, 353, 533, 741, 1009, 1330, 1743, 2176, 2768, 3360, 4133, 4930, 5815, 6843, 7928, 9161, 10510, 12014, 13675, 15367, 17308, 19360, 21660, 24009, 26558, 29303, 32307, 35259, 38668, 42073, 45802, 49619, 53900, 58137, 62849, 67650, 72699
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.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=589; 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. A273111.
Sequence in context: A272926 A272945 A272997 * A273177 A055195 A343497
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 15 2016
STATUS
approved