[seqfan] Simple formulas for Madelung constants?

[jonscho at hiwaay.net]

The Formula section of A085469 gives a formula of the form

      Sum_{i, j, k not all 0} f(i,j,k)

(In this case, f(i,j,k) = (-1)^(i+j+k)/sqrt(i^2+j^2+k^2).)

Is there a similar formula (differing only in its function f(i,j,k))  
for A181152, A182565, A182566, or A182567?

Thanks!

-- Jon