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A272922
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 555", based on the 5-celled von Neumann neighborhood.
1
1, 6, 23, 52, 113, 202, 331, 480, 701, 982, 1335, 1740, 2241, 2810, 3467, 4136, 4965, 5918, 7007, 8212, 9577, 11074, 12723, 14448, 16389, 18494, 20783, 23180, 25801, 28546, 31459, 34296, 37493, 40942, 44655, 48612, 52857, 57362, 62147, 67136, 72469, 78094
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=555; 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. A272920.
Sequence in context: A212570 A272840 A272941 * A234729 A273500 A189713
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 10 2016
STATUS
approved