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A272579
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 502", based on the 5-celled von Neumann neighborhood.
1
1, 6, 14, 38, 67, 115, 171, 276, 352, 500, 641, 885, 1030, 1274, 1574, 1971, 2315, 2763, 3224, 3824, 4321, 4966, 5654, 6530, 7247, 8171, 9103, 10216, 11224, 12480, 13812, 15184, 16609, 18205, 19781, 21714, 23310, 25314, 27435, 29591, 31579, 34128, 36596
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=502; 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. A272577.
Sequence in context: A270187 A271459 A271010 * A274896 A330832 A134259
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 03 2016
STATUS
approved