Is there a non recursive formula for mixed resistors?
It's to do with the golden ratio I think: -



or...



For N = 1, 

x = \$\dfrac{13}{8}+\dfrac{-1^{2} \cdot 3!}{3!\cdot 1!\cdot 4^{5}}\$ = 

x = \$\dfrac{13}{8}+\dfrac{3!}{3!\cdot 4^{5}}\$ = 1.6259765625

Anyway the link is here and I can't vouch for it being perfect.