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A271059
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 260", based on the 5-celled von Neumann neighborhood.
1
3, 1, 7, -8, 12, 4, 28, -31, 7, 12, 44, -68, 36, 12, 84, -104, 16, 52, 92, -144, 16, 68, 60, -44, 20, 56, 136, -228, 92, 104, 104, -124, -12, 84, 156, -228, 28, 20, 100, -4, -36, 84, 76, -136, 40, 292, 28, -120, -64, 168, 328, -384, 48, 76, 380, -364, 212
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
First Differences of A253086.
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=260; 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. A253086.
Sequence in context: A217594 A340616 A120472 * A121370 A137908 A229837
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 29 2016
STATUS
approved