login
A273575
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 801", based on the 5-celled von Neumann neighborhood.
1
1, 5, 22, 50, 107, 191, 308, 448, 653, 917, 1234, 1634, 2099, 2611, 3192, 3844, 4593, 5521, 6494, 7698, 9027, 10415, 11912, 13568, 15345, 17341, 19442, 21754, 24167, 26603, 29132, 31804, 34789, 38005, 41434, 45298, 49303, 53503, 57856, 62548, 67581, 72957
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=801; 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. A273573.
Sequence in context: A273121 A099078 A272836 * A272848 A273612 A272937
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 25 2016
STATUS
approved