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A273764
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 910", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 32, 53, 82, 119, 188, 277, 362, 451, 604, 805, 1002, 1227, 1520, 1841, 2142, 2435, 2824, 3249, 3590, 3971, 4468, 4973, 5470, 6011, 6728, 7513, 8258, 9071, 10060, 11125, 12094, 13087, 14288, 15513, 16590, 17667, 18776, 20025, 21298, 22583, 24020
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=910; 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. A273762.
Sequence in context: A143274 A273332 A273427 * A273853 A192747 A231264
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 29 2016
STATUS
approved