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A270154
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 97", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 46, 59, 143, 164, 336, 361, 633, 682, 1090, 1171, 1743, 1816, 2620, 2749, 3693, 3846, 5078, 5242, 6759, 6903, 8767, 8992, 11052, 11289, 13857, 14173, 16990, 17310, 20519, 20891, 24591, 25027, 29183, 29651, 34255, 34791, 39879, 40531, 46275, 47051
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=97; 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. A270152.
Sequence in context: A270661 A222908 A270911 * A271307 A270162 A271416
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 12 2016
STATUS
approved