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A270334
Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 158", based on the 5-celled von Neumann neighborhood.
0
1, 5, 20, 52, 236, 916, 4060, 16904, 66660, 265800, 1059724, 4219684, 16816424, 67131892, 268216416, 1072151796
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
(* From Robert Price, Start *)
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 158; 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 *)
(* From Robert Price, End *)
Total[#, 2] & /@ Array[CellularAutomaton[{158, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, {{{2^# - 1}}}] &, 6] (* JungHwan Min, Mar 16 2016 *)
CROSSREFS
Cf. A270333.
Sequence in context: A102227 A173034 A006010 * A008524 A055383 A090133
KEYWORD
nonn,more
AUTHOR
Robert Price, Mar 15 2016
EXTENSIONS
a(8)-a(15) from Lars Blomberg, May 07 2016
STATUS
approved