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A271120
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 283", based on the 5-celled von Neumann neighborhood.
1
4, 0, 39, -39, 104, -93, 197, -208, 336, -316, 487, -495, 668, -624, 847, -871, 1140, -1124, 1399, -1395, 1656, -1600, 1943, -1943, 2324, -2324, 2711, -2675, 3095, -3055, 3520, -3536, 4084, -4041, 4521, -4493, 5057, -5069, 5605, -5473, 6033, -6041, 6693
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=283; 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. A271117.
Sequence in context: A270184 A375413 A271300 * A174083 A123936 A271834
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved