Triangular Square Numbers
Python 2, 45 - 4 - 4 = 37



a=1;b=0
exec"a,b=b,34*b-a+2;"*input()
print a


Iterates using the reccurence

f(0) = 1
f(1) = 0
f(k) = 34*f(k-1)-f(k-2)+2


In theory, this supports numbers of any size, but runs in exponential time, so it shouldn't qualify for the bonuses. Should work for numbers of any size. For example, for 100, gives

1185827220993342542557325920096705939276583904852110550753333094088280194260929920844987597980616456388639477930416411849864965254621398934978872054025


A recursive solution uses 41 chars, but shouldn't qualify because it takes exponential time.

f=lambda k:k&gt;2and 34*f(k-1)-f(k-2)+2or~-k