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A273490
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 758", based on the 5-celled von Neumann neighborhood.
1
1, 6, 15, 36, 69, 114, 175, 260, 389, 546, 735, 956, 1237, 1546, 1903, 2316, 2805, 3354, 3967, 4644, 5413, 6242, 7151, 8140, 9237, 10410, 11679, 13028, 14501, 16034, 17679, 19444, 21349, 23378, 25535, 27820, 30261, 32826, 35535, 38388, 41413, 44578, 47903
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=758; 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. A273486.
Sequence in context: A269543 A074149 A273411 * A324221 A177206 A128443
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved