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\begin{abstract}
Shapiro gave a combinatorial proof of a bilinear generating function for Chebyshev
    polynomials equivalent to the formula
\[ \frac{1}{1-ax-x^2}\ast \frac{1}{1-bx-x^2}
                =  \frac{1-x^2}{1-abx-(2+a^2+b^2)x^2
                -abx^3+x^4},  \]
    where $*$ denotes the Hadamard product. In a similar way, by considering tilings of a $2\times n$ rectangle
    with $1\times1$ and $1\times 2$ bricks in the top row, and $1\times1$ and $1\times n$ bricks in the bottom row,
    we find an explicit formula for the
    Hadamard product
    \[\frac{1}{1-ax-x^2}\ast \frac{x^m}{1-bx-x^n}.\]
\end{abstract}

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