Calculating the Number of Squares Inside a Circle in the 1st Quadrant

[Wilmer]

A 10by10 square contains 100 1by1 squares (of course!).
A circle is drawn inside above square, tangent to all 4 sides.
How many of the 1by1 squares are fully inside the circle?

I get 60...which I think is correct.
Trying to devise a general case formula...

 

[Wilmer]

Couldn't come up with general case formula.

However, this simple program seems to work:

-center of circle at origin
-examine the 1/4 circle in 1st quadrant

r = radius
x,y = points on circumference

INPUT r
LOOP x FROM 1 TO r
y = FLOOR[SQRT(r^2 - x^2)]
count = count + y
ENDLOOP
PRINT count*4

See anything wrong?