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A273028
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 579", based on the 5-celled von Neumann neighborhood.
1
1, 6, 19, 48, 105, 178, 299, 432, 641, 854, 1155, 1492, 1925, 2374, 2999, 3576, 4353, 5122, 6019, 7020, 8181, 9318, 10831, 12216, 13861, 15634, 17479, 19496, 21749, 23950, 26651, 29220, 32085, 34962, 38231, 41520, 45033, 48802, 52907, 56880, 61473, 66006
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=579; 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. A273026.
Sequence in context: A034199 A272752 A272803 * A273079 A073362 A095264
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 13 2016
STATUS
approved