Sample input points (T(n) vs. n): 

 

> input := [[1,2],[2,5],[3,10],[4,17],[5,26],[6,37],[7,50],[8,65]];
 

[[1, 2], [2, 5], [3, 10], [4, 17], [5, 26], [6, 37], [7, 50], [8, 65]] (1)
 

> with( plots ):
 

Let's look at T(n) vs. n: 

 

> plot( input, n=0..8, style=point, symbolsize=15 );
 

Plot_2d
 

 

Increasing.  So, ω(1) (bound below by constant, not tightly).  Let's consider T(n)/n vs. n 

 

I'll provide a procedure that can be passed to map.  Given a point [x,y] and a function, e.g., n->n^2, returns the point [x, y/func(x)] 

 

> applyPoint := proc( point, func )  local x, y;
 description "Divides y by func(x)";
 x := point[1]; y := point[2];
 [ x, y/func(x) ];
end proc:
 

 

 

Here is another function, for your convenience.  Takes a list of points and a function, returns a list of points, [x, y/func(x)] 

 

> pointMapFamily := proc( points, func )
 description "plotPoints( points, func ) plots points (x, func(y))";
 map( applyPoint, points, func)
end proc:
 

 

Take another stab at the data above.  Divide by n: 

 

> guess_n := pointMapFamily( input, n->n );
 

[[1, 2], [2, `/`(5, 2)], [3, `/`(10, 3)], [4, `/`(17, 4)], [5, `/`(26, 5)], [6, `/`(37, 6)], [7, `/`(50, 7)], [8, `/`(65, 8)]] (2)
 

> plot( guess_n, n=0..8, style=point, symbolsize=15 );
 

Plot_2d
 

 

Nope, still increasing.  So, T(n) = ω(n) (T(n) is bound below by a line, but not tightly) 

 

Try T(n) / n^2: 

 

> guess_n_2 := pointMapFamily( input, n->n^2 );
 

[[1, 2], [2, `/`(5, 4)], [3, `/`(10, 9)], [4, `/`(17, 16)], [5, `/`(26, 25)], [6, `/`(37, 36)], [7, `/`(50, 49)], [8, `/`(65, 64)]] (3)
 

> plot( guess_n_2, n=0..8, style=point, symbolsize=15 );
 

Plot_2d
 

 

Shoot, going to 0.  Or is it?  Look more closely: 

 

> plot( guess, n=0..8, 0..3, style=point, symbolsize=15 );
 

Plot_2d
 

How 'bout that?  Looks as if T(n) = Typesetting:-mrow(Typesetting:-mi( 

 

Let's look at  this with the line y=1 

 

> ourPoints := plot( guess, n=0..8, 0..3, style=point, symbolsize=15, color=blue ):
 

> asym := plot( 1, n=0..10 ):
 

> display( { ourPoints, asym } );
 

Plot_2d