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A273681
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 838", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 28, 33, 58, 75, 136, 145, 190, 235, 364, 413, 538, 627, 856, 945, 1142, 1251, 1532, 1665, 2022, 2227, 2720, 2929, 3366, 3647, 4360, 4653, 5370, 5795, 6708, 7277, 8058, 8727, 9716, 10513, 11694, 12603, 13972, 14773, 16142, 17163, 18696, 19909, 21506
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=838; 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. A273544.
Sequence in context: A253908 A273504 A273608 * A273705 A165819 A087737
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved