login
A273332
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 654", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 32, 53, 82, 119, 188, 261, 342, 431, 552, 681, 842, 1027, 1308, 1593, 1886, 2187, 2520, 2861, 3234, 3631, 4124, 4629, 5158, 5711, 6360, 7033, 7802, 8643, 9772, 10905, 12046, 13195, 14376, 15565, 16786, 18031, 19372, 20725, 22102, 23503, 25000
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=654; 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. A273330.
Sequence in context: A273117 A273689 A143274 * A273427 A273764 A273853
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 20 2016
STATUS
approved