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A273685
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 841", based on the 5-celled von Neumann neighborhood.
1
1, 5, 22, 59, 120, 217, 341, 518, 746, 1055, 1392, 1801, 2293, 2906, 3534, 4287, 5147, 6192, 7240, 8417, 9765, 11330, 12882, 14587, 16503, 18628, 20864, 23281, 25921, 28870, 31770, 34947, 38419, 42192, 46044, 50093, 54441, 59166, 63890, 68875, 74119, 79708
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=841; 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. A273683.
Sequence in context: A208946 A245301 A256971 * A050533 A212094 A064836
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved