login
A271257
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 324", based on the 5-celled von Neumann neighborhood.
1
1, 5, 10, 22, 30, 54, 79, 119, 152, 196, 236, 324, 401, 501, 622, 798, 935, 1099, 1240, 1444, 1661, 1949, 2258, 2642, 2995, 3399, 3800, 4308, 4821, 5385, 5986, 6710, 7411, 8083, 8812, 9636, 10485, 11449, 12430, 13598, 14727, 15851, 16964, 18232, 19573, 20997
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=324; 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. A246316.
Sequence in context: A132461 A255150 A266580 * A343456 A087746 A064694
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 02 2016
STATUS
approved