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A273705
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 870", based on the 5-celled von Neumann neighborhood.
1
1, 6, 11, 28, 33, 58, 75, 136, 145, 190, 235, 364, 421, 562, 679, 964, 1085, 1294, 1511, 1828, 2093, 2486, 2883, 3508, 4009, 4570, 5187, 5984, 6681, 7562, 8407, 9504, 10437, 11502, 12643, 13912, 15009, 16334, 17695, 19308, 20849, 22526, 24199, 26108, 28053
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=870; 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. A273703.
Sequence in context: A273504 A273608 A273681 * A165819 A087737 A273328
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 28 2016
STATUS
approved