  Searches for new heavy resonances decaying into different pairings of $W$,
$Z$, or Higgs bosons, as well as directly into leptons, are presented using a
data sample corresponding to 36.1fb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ =
13 TeV collected during 2015 and 2016 with the ATLAS detector at the CERN Large
Hadron Collider. Analyses selecting bosonic decay modes in the $qqqq$, $\nu\nu
qq$, $\ell\nu qq$, $\ell\ell qq$, $\ell\nu\ell\nu$, $\ell\ell\nu\nu$,
$\ell\nu\ell\ell$, $\ell\ell\ell\ell$, $qqbb$, $\nu\nu bb$, $\ell\nu bb$, and
$\ell\ell bb$ final states are combined, searching for a narrow-width
resonance. Likewise, analyses selecting the leptonic $\ell\nu$ and $\ell\ell$
final states are also combined. These two sets of analyses are then further
combined. No significant deviation from the Standard Model predictions is
observed. Three benchmark models are tested: a model predicting the existence
of a new heavy scalar singlet, a simplified model predicting a heavy
vector-boson triplet, and a bulk Randall-Sundrum model with a heavy spin-2
Kaluza-Klein excitation of the graviton. Cross-section limits are set at the
95% confidence level using an asymptotic approximation and are compared with
predictions for the benchmark models. These limits are also expressed in terms
of constraints on couplings of the heavy vector-boson triplet to quarks,
leptons, and the Higgs boson. The data exclude a heavy vector-boson triplet
with mass below 5.5 TeV in a weakly coupled scenario and 4.5 TeV in a strongly
coupled scenario, as well as a Kaluza-Klein graviton with mass below 2.3 TeV.
