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A270932
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 219", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 48, 56, 153, 178, 363, 396, 725, 773, 1234, 1298, 1939, 2056, 2873, 2982, 4115, 4272, 5637, 5798, 7439, 7664, 9545, 9801, 12158, 12491, 15244, 15665, 18854, 19299, 22772, 23269, 27318, 27823, 32464, 33005, 38102, 38786, 44447, 45163, 51548, 52324
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=219; 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. A270930.
Sequence in context: A270292 A270899 A270327 * A269816 A270020 A269878
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 26 2016
STATUS
approved