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A272317
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 465", based on the 5-celled von Neumann neighborhood.
1
3, 5, 19, -3, 59, -35, 91, -51, 171, -147, 267, -219, 371, -299, 387, -275, 523, -499, 747, -699, 979, -907, 1123, -1003, 1347, -1275, 1555, -1411, 1723, -1507, 1563, -1235, 1739, -1715, 2219, -2171, 2707, -2635, 3107, -2987, 3587, -3515, 4051, -3907, 4475
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=465; 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. A272313.
Sequence in context: A145774 A348778 A270894 * A128362 A272283 A053484
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 25 2016
STATUS
approved