A famous problem in symmetric function theory is to find combinatorial formulas for Schur expansions of the Macdonald polynomials
H
~
μ
\tilde {H}_{\mu }
. One such formula, valid for
μ
\mu
satisfying
μ
1
≤
3
\mu _1\leq 3
and
μ
2
≤
2
\mu _2\leq 2
, involves Yamanouchi words weighted by Haglund’s statistics
inv
μ
\operatorname {inv}_{\mu }
and
maj
μ
\operatorname {maj}_{\mu }
. Previous proofs of this formula use the technical machinery of crystals and dual equivalence graphs. We give a new, elementary, and fully bijective proof of this formula based on the abacus model for antisymmetrized Macdonald polynomials. An extension to the Schur expansion of
s
ν
H
~
μ
s_{\nu }\tilde {H}_{\mu }
is also provided.