login
A270288
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 145", based on the 5-celled von Neumann neighborhood.
1
1, 5, 10, 42, 46, 147, 167, 324, 328, 669, 689, 1150, 1166, 1815, 1895, 2584, 2588, 3793, 3813, 5266, 5282, 7051, 7131, 9068, 9084, 11605, 11685, 14438, 14502, 17663, 17983, 20864, 20868, 25337, 25357, 30330, 30346, 35891, 35971, 41940, 41956, 48765, 48845
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=145; 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. A270286.
Sequence in context: A364738 A136138 A321307 * A271805 A269812 A271127
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 14 2016
STATUS
approved