  We explore the impact of outer stellar companions on the occurrence rate of
giant planets detected with radial velocities. We searched for stellar and
planetary companions to a volume-limited sample of solar-type stars within 25
pc. Using adaptive optics imaging from the Lick 3m and Palomar 200" Telescopes,
we characterized the multiplicity of our sample stars, down to the bottom of
the main sequence. With these data, we confirm field star multiplicity
statistics from previous surveys. We combined three decades of radial velocity
data from the California Planet Search with new RV data from Keck/HIRES and
APF/Levy to search for planets in the same systems. Using an updated catalog of
both stellar and planetary companions and injection/recovery tests to determine
our sensitivity, we measured the occurrence rate of planets among the single
and multiple star systems. We found that planets with masses of 0.1-10
$M_{Jup}$ and semi-major axes of 0.1-10 AU have an occurrence rate of
$0.18^{+0.04}_{-0.03}$ planets per single star, and $0.12\pm0.04$ planets per
binary primary. Only one planet-hosting binary system in our sample had a
binary separation $<100$ AU, and none had a separation $<50$ AU. We found
planet occurrence rates of $0.20^{+0.07}_{-0.06}$ planets per star for binaries
with separation $a_B > 100$ AU, and $0.04^{+0.04}_{-0.02}$ planets per star for
binaries with separation $a_B<100$ AU. The similarity in the planet occurrence
rate around single stars and wide primaries implies that wide binary systems
should host more planets than single star systems, since they have more
potential host stars. We estimated a system-wide planet occurrence rate of 0.3
planets per wide binary system for binaries with separations $a_B > 100$ AU.
Finally, we found evidence that giant planets in binary systems have a
different semi-major axis distribution than their counterparts in single star
systems.
