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A272707
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 515", based on the 5-celled von Neumann neighborhood.
1
1, 6, 19, 44, 93, 162, 271, 408, 601, 830, 1131, 1476, 1909, 2394, 2983, 3632, 4401, 5238, 6211, 7260, 8461, 9746, 11199, 12744, 14473, 16302, 18331, 20468, 22821, 25290, 27991, 30816, 33889, 37094, 40563, 44172, 48061, 52098, 56431, 60920, 65721, 70686
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=515; 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. A272705.
Sequence in context: A299264 A183763 A209403 * A266938 A362602 A299265
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 04 2016
STATUS
approved