login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A271458
Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 374", based on the 5-celled von Neumann neighborhood.
0
1, 5, 24, 92, 381, 1365, 5048, 20908, 84064, 339648, 1387316, 5668180, 23008784, 92903476, 373975168, 1502833016
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=374; 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 *)
Part[on, 2^Range[0, Log[2, stages]]] (* Extract relevant terms *)
CROSSREFS
Cf. A169701.
Sequence in context: A074085 A145914 A066316 * A301526 A180354 A212349
KEYWORD
nonn,more
AUTHOR
Robert Price, Apr 08 2016
EXTENSIONS
a(8)-a(15) from Lars Blomberg, Jun 17 2016
STATUS
approved