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A272048
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 419", based on the 5-celled von Neumann neighborhood.
1
4, 8, 15, -3, 76, -45, 113, -73, 169, -128, 204, -200, 412, -320, 504, -404, 524, -504, 704, -628, 924, -869, 1101, -969, 1225, -1148, 1368, -1308, 1796, -1660, 2028, -1784, 2008, -2004, 2360, -2180, 2700, -2648, 3184, -2892, 3108, -3112, 3620, -3424, 3976
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=419; 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. A272045.
Sequence in context: A242519 A174554 A360527 * A112312 A076343 A335382
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 18 2016
STATUS
approved