login
A272009
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 413", based on the 5-celled von Neumann neighborhood.
1
1, 9, 14, 62, 67, 187, 192, 416, 421, 781, 786, 1314, 1319, 2047, 2052, 3012, 3017, 4241, 4246, 5766, 5771, 7619, 7624, 9832, 9837, 12437, 12442, 15466, 15471, 18951, 18956, 22924, 22929, 27417, 27422, 32462, 32467, 38091, 38096, 44336, 44341, 51229, 51234
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=413; 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. A272007.
Sequence in context: A272113 A272293 A272545 * A298754 A166654 A348318
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 17 2016
STATUS
approved