login
A271545
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 387", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 39, 56, 140, 181, 305, 362, 670, 735, 1111, 1252, 1756, 1881, 2513, 2662, 3582, 3867, 4919, 5176, 6508, 6789, 8353, 8686, 10614, 11103, 13143, 13776, 16292, 16909, 19533, 20238, 23578, 24279, 27859, 28876, 32748, 33777, 38413, 39258, 44390, 45555
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=387; 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. A271543.
Sequence in context: A299267 A254008 A277089 * A272258 A192308 A277237
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 09 2016
STATUS
approved