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A272312
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood.
1
4, 3, 13, -1, 12, 16, 17, -9, 28, 0, 28, 24, 60, 20, 81, -53, 56, 8, -40, 88, 40, 72, 104, -48, 20, 72, 128, 52, 104, 60, 185, -133, 72, -32, 68, 68, 80, 208, 116, 76, -48, 164, -8, 84, 180, 104, 360, -20, -68, 56, 136, -36, 260, 176, 284, -120, 212, 76, 64
OFFSET
0,1
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=462; 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[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A246330.
Sequence in context: A271696 A271090 A271284 * A272117 A271159 A268276
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 25 2016
STATUS
approved