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A273581
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 825", based on the 5-celled von Neumann neighborhood.
1
1, 5, 22, 50, 111, 204, 345, 502, 723, 1019, 1412, 1817, 2297, 2874, 3567, 4300, 5157, 6182, 7327, 8624, 10021, 11618, 13255, 15020, 16985, 19130, 21359, 23792, 26481, 29162, 32143, 35224, 38613, 42150, 46135, 50516, 54929, 59710, 64679, 69784, 75205, 80898
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=825; 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. A273430.
Sequence in context: A272937 A273648 A272993 * A049452 A273075 A272824
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved