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A273648
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 817", based on the 5-celled von Neumann neighborhood.
1
1, 5, 22, 50, 111, 200, 321, 481, 714, 999, 1356, 1757, 2266, 2795, 3416, 4052, 4901, 5902, 7011, 8268, 9645, 11094, 12695, 14364, 16177, 18274, 20395, 22692, 25237, 27858, 30647, 33475, 36684, 40149, 43858, 47863, 52124, 56501, 61170, 65815, 70848, 76221
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=817; 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. A273646.
Sequence in context: A272848 A273612 A272937 * A272993 A273581 A049452
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved