  The Manin-Peyre conjecture is established for smooth spherical Fano
threefolds of semisimple rank one and type N. Together with the previously
solved case T and the toric cases, this covers all types of smooth spherical
Fano threefolds. The case N features a number of structural novelties; most
notably, one may lose regularity of the ambient toric variety, the height
conditions may contain fractional exponents, and it may be necessary to exclude
a thin subset with exceptionally many rational points from the count, as
otherwise Manin's conjecture in its original form would turn out to be
incorrect.
