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A273504
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 774", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 28, 33, 58, 75, 136, 145, 190, 235, 360, 401, 558, 631, 852, 909, 1050, 1179, 1488, 1613, 1918, 2043, 2448, 2581, 3062, 3307, 3904, 4237, 4834, 5231, 6024, 6453, 7134, 7747, 8716, 9277, 10170, 10839, 11832, 12653, 13714, 14607, 15920, 16793, 18222
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=774; 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. A273502.
Sequence in context: A061725 A105708 A253908 * A273608 A273681 A273705
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved