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A270990
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 241", based on the 5-celled von Neumann neighborhood.
1
1, 5, 18, 54, 91, 179, 256, 412, 525, 809, 930, 1362, 1591, 2151, 2488, 3224, 3529, 4601, 4962, 6150, 6751, 8203, 8880, 10648, 11501, 13645, 14410, 16910, 18031, 20859, 22096, 25228, 26497, 30333, 31554, 35634, 37419, 41971, 43615, 48779, 50824, 56416, 58644
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=241; 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. A270988.
Sequence in context: A178684 A353689 A271771 * A272558 A081492 A263318
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 27 2016
STATUS
approved