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A272941
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 563", based on the 5-celled von Neumann neighborhood.
1
1, 6, 23, 52, 113, 202, 323, 484, 701, 970, 1319, 1732, 2209, 2782, 3411, 4112, 4929, 5858, 6955, 8180, 9521, 10974, 12583, 14356, 16253, 18330, 20559, 22916, 25461, 28142, 30891, 33768, 36913, 40370, 44027, 47908, 52061, 56446, 61095, 66048, 71157, 76474
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=563; 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. A272939.
Sequence in context: A022269 A212570 A272840 * A272922 A234729 A273500
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 11 2016
STATUS
approved