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A270331
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 157", based on the 5-celled von Neumann neighborhood.
1
1, 9, 13, 57, 62, 178, 190, 399, 411, 767, 787, 1291, 1308, 2020, 2064, 2964, 3017, 4205, 4253, 5721, 5790, 7582, 7718, 9814, 9967, 12455, 12619, 15531, 15732, 19064, 19301, 23081, 23341, 27657, 27889, 32714, 33018, 38399, 38723, 44732, 45136, 51661, 52153
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=157; 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. A270329.
Sequence in context: A270982 A323797 A270319 * A270628 A270679 A270903
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 15 2016
STATUS
approved