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A272700
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 510", based on the 5-celled von Neumann neighborhood.
1
1, 6, 18, 43, 71, 127, 183, 296, 356, 476, 596, 836, 956, 1196, 1436, 1917, 2041, 2289, 2537, 3033, 3281, 3777, 4273, 5265, 5513, 6009, 6505, 7497, 7993, 8985, 9977, 11962, 12214, 12718, 13222, 14230, 14734, 15742, 16750, 18766, 19270, 20278, 21286, 23302
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=510; 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. A169699.
Sequence in context: A068293 A334839 A272250 * A191101 A184630 A009957
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 04 2016
STATUS
approved