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A273297
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 629", based on the 5-celled von Neumann neighborhood.
1
1, 9, 29, 74, 135, 247, 379, 580, 805, 1153, 1537, 2022, 2507, 3187, 3863, 4756, 5657, 6810, 7923, 9308, 10613, 12337, 13913, 15906, 17731, 20135, 22375, 25112, 27633, 30841, 33821, 37490, 40807, 44883, 48611, 53304, 57541, 62661, 67321, 73126, 78539, 84891
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=629; 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. A273295.
Sequence in context: A055195 A343497 A273243 * A273268 A273306 A318742
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 19 2016
STATUS
approved