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A272587
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 507", based on the 5-celled von Neumann neighborhood.
1
1, 6, 19, 59, 88, 188, 257, 457, 542, 866, 999, 1479, 1660, 2304, 2613, 3485, 3810, 4934, 5307, 6715, 7136, 8836, 9401, 11449, 12062, 14466, 15223, 18015, 18916, 22056, 23357, 26981, 28298, 32430, 33795, 38467, 39880, 45100, 46657, 52481, 54086, 60522, 62271
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=507; 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. A272585.
Sequence in context: A057571 A238055 A272227 * A125069 A080926 A184189
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 03 2016
STATUS
approved