login
A273075
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 585", based on the 5-celled von Neumann neighborhood.
1
1, 5, 22, 51, 100, 181, 314, 439, 615, 864, 1165, 1502, 1903, 2388, 2973, 3582, 4291, 5076, 5973, 6966, 8107, 9404, 10841, 12350, 14035, 15760, 17657, 19566, 21767, 24196, 26841, 29362, 32154, 35083, 38344, 41532, 45025, 48726, 52847, 56956, 61333, 65826
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=585; 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. A273073.
Sequence in context: A272993 A273581 A049452 * A272824 A373110 A273677
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 14 2016
STATUS
approved