login
A270463
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 169", based on the 5-celled von Neumann neighborhood.
1
1, 5, 14, 38, 67, 135, 176, 296, 389, 617, 690, 1034, 1223, 1675, 1816, 2428, 2745, 3497, 3818, 4798, 5259, 6399, 6768, 8288, 8845, 10561, 11182, 13186, 13887, 16147, 16912, 19444, 20565, 23525, 24402, 27798, 29099, 32739, 34068, 38340, 40001, 44545, 45834
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=169; 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. A270461.
Sequence in context: A270687 A272254 A270452 * A183898 A225865 A319648
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 17 2016
STATUS
approved