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A271135
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 294", based on the 5-celled von Neumann neighborhood.
1
4, -1, 16, -11, 24, -16, 56, -48, 48, -40, 64, -40, 96, -88, 160, -148, 144, -140, 184, -188, 208, -188, 328, -320, 328, -224, 360, -360, 392, -284, 504, -412, 504, -556, 464, -396, 480, -404, 608, -528, 664, -636, 728, -692, 648, -472, 936, -864, 920, -1044
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=294; 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. A271133.
Sequence in context: A143697 A374098 A272088 * A271601 A271068 A272509
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved