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A271166
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 307", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 47, 60, 164, 189, 381, 430, 746, 787, 1227, 1336, 1960, 2029, 2885, 3066, 4138, 4323, 5663, 5872, 7493, 7741, 9682, 10018, 12335, 12623, 15224, 15664, 18769, 19142, 22643, 23211, 27092, 27760, 32081, 32770, 37574, 38279, 43755, 44708, 50652, 51481
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=307; 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. A271164.
Sequence in context: A244023 A271131 A271154 * A271248 A271399 A268154
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved