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A272793
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 537", based on the 5-celled von Neumann neighborhood.
1
3, 9, 15, 21, 32, 7, 85, 20, 60, -5, 149, 11, 125, -21, 229, 8, 148, -40, 295, 24, 149, -36, 432, -172, 411, -135, 372, 23, 353, -257, 677, -57, 357, -245, 733, -125, 596, -283, 764, -296, 720, -372, 895, -367, 852, -412, 908, -308, 880, -517, 1161, -112
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=537; 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. A272790.
Sequence in context: A272749 A273560 A246388 * A273567 A162486 A067201
KEYWORD
sign,easy
AUTHOR
Robert Price, May 06 2016
STATUS
approved