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A272019
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 417", based on the 5-celled von Neumann neighborhood.
1
3, 5, 19, -11, 51, -27, 99, -107, 227, -159, 239, -279, 475, -367, 451, -555, 963, -831, 975, -987, 1095, -915, 1051, -1251, 1931, -1623, 1671, -1835, 2203, -1875, 1911, -2239, 3235, -2815, 2795, -2975, 3371, -2947, 2967, -3295, 4283, -3747, 3747, -4083
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=417; 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. A272016.
Sequence in context: A272283 A053484 A272092 * A270723 A242961 A025046
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 17 2016
STATUS
approved