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A272014
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 414", based on the 5-celled von Neumann neighborhood.
1
1, 6, 18, 39, 71, 111, 192, 244, 340, 448, 641, 773, 990, 1186, 1515, 1735, 2075, 2403, 2915, 3284, 3789, 4313, 5049, 5537, 6389, 7030, 8014, 8842, 9871, 10779, 12184, 13160, 14449, 15645, 17358, 18618, 20291, 21664, 23624, 25132, 27256, 28988, 31428, 33317
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=414; 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. A272012.
Sequence in context: A261651 A270215 A129863 * A272453 A370349 A271252
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 17 2016
STATUS
approved