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A268154
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 363", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 47, 64, 165, 205, 358, 407, 716, 788, 1217, 1330, 1922, 2067, 2875, 2984, 4060, 4265, 5526, 5718, 7363, 7660, 9516, 9773, 12033, 12398, 14934, 15359, 18319, 18808, 22164, 22541, 26482, 27062, 31267, 31839, 36692, 37364, 42637, 43277, 49274, 50142
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=363; 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. A264099.
Sequence in context: A271166 A271248 A271399 * A271456 A271537 A271891
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 07 2016
STATUS
approved