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A272151
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 435", based on the 5-celled von Neumann neighborhood.
1
1, 6, 19, 55, 88, 180, 245, 430, 506, 795, 931, 1352, 1573, 2138, 2398, 3183, 3476, 4496, 4865, 6109, 6638, 8142, 8747, 10551, 11224, 13328, 14185, 16605, 17614, 20458, 21715, 25044, 26392, 30069, 31382, 35646, 37079, 41691, 43508, 48712, 50665, 56301, 58606
OFFSET
0,2
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=435; 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[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
CROSSREFS
Cf. A272149.
Sequence in context: A273142 A273173 A127642 * A272562 A176883 A274599
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 21 2016
STATUS
approved