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A272508
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 486", based on the 5-celled von Neumann neighborhood.
1
1, 6, 10, 30, 39, 76, 104, 161, 202, 274, 375, 527, 675, 879, 1123, 1455, 1736, 2053, 2341, 2709, 3157, 3650, 4206, 4918, 5627, 6355, 7148, 8024, 8949, 9909, 10954, 12282, 13555, 14824, 16081, 17518, 18947, 20552, 22305, 24226, 26223, 28216, 30369, 32694
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=486; 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. A272506.
Sequence in context: A271261 A271412 A272278 * A218553 A265857 A256865
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 01 2016
STATUS
approved