  We introduce a unary coding of bosonic occupation states based on the famous
"balls and walls" counting for the number of configurations of $N$
indistinguishable particles on $L$ distinguishable sites. Each state is
represented by an integer with a human readable bit string that has a
compositional structure allowing for the efficient application of operators
that locally modify the number of bosons. By exploiting translational and
inversion symmetries, we identify a speedup factor of order $L$ over current
methods when generating the basis states of bosonic lattice models. The unary
coding is applied to a one-dimensional Bose-Hubbard Hamiltonian with up to
$L=N=20$, and the time needed to generate the ground state block is reduced to
a fraction of the diagonalization time. For the ground state symmetry resolved
entanglement, we demonstrate that variational approaches restricting the local
bosonic Hilbert space could result in an error that scales with system size.
