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A271605
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 393", based on the 5-celled von Neumann neighborhood.
1
3, 1, 23, -19, 75, -55, 107, -119, 263, -235, 331, -327, 479, -411, 487, -499, 767, -723, 927, -907, 1191, -1171, 1415, -1371, 1663, -1635, 1943, -1811, 1991, -1939, 2151, -2107, 2519, -2443, 2863, -2891, 3503, -3451, 3903, -3891, 4495, -4451, 4991, -4843
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=393; 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. A271602.
Sequence in context: A243769 A137330 A270277 * A270220 A281377 A138654
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 10 2016
STATUS
approved