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A273455
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 734", based on the 5-celled von Neumann neighborhood.
1
1, 6, 19, 40, 73, 122, 183, 264, 377, 518, 675, 844, 1057, 1318, 1583, 1916, 2337, 2814, 3255, 3796, 4397, 5090, 5815, 6612, 7617, 8686, 9747, 10928, 12221, 13602, 14951, 16444, 18193, 20022, 21819, 23816, 26013, 28274, 30615, 33100, 35945, 38862, 41707
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=734; 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. A273453.
Sequence in context: A272811 A273206 A273394 * A273571 A273778 A173980
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 22 2016
STATUS
approved