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A272275
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 453", based on the 5-celled von Neumann neighborhood.
1
1, 9, 14, 54, 71, 175, 204, 392, 441, 741, 802, 1262, 1355, 1947, 2096, 2904, 3021, 4085, 4282, 5550, 5787, 7363, 7592, 9472, 9757, 11945, 12242, 14778, 15187, 18139, 18580, 21928, 22465, 26305, 26790, 31058, 31735, 36515, 37248, 42428, 43293, 49193, 49986
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=453; 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. A272273.
Sequence in context: A027009 A239038 A271596 * A272051 A272504 A346267
KEYWORD
nonn,easy,changed
AUTHOR
Robert Price, Apr 24 2016
STATUS
approved