login
A273423
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 710", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 28, 37, 66, 83, 144, 161, 238, 275, 388, 437, 586, 627, 776, 833, 1102, 1179, 1492, 1589, 1954, 2067, 2480, 2621, 3110, 3259, 3772, 3997, 4674, 4863, 5520, 5769, 6662, 6911, 7804, 8165, 9122, 9379, 10336, 10685, 11902, 12311, 13652, 14089, 15682
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=710; 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. A273421.
Sequence in context: A165819 A087737 A273328 * A273760 A273837 A273409
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 22 2016
STATUS
approved