  Louis W. Shapiro gave a combinatorial proof of a bilinear generating function
for Chebyshev polynomials equivalent to the formula 1/(1-ax-x^2) * 1/(1-bx-x^2)
= (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 by n rectangle with 1
by 1 and 1 by 2 bricks in the top row, and 1 by 1 and 1 by n bricks in the
bottom row, we find an explicit formula for the Hadamard product 1/(1-ax-x^2) *
x^m/(1-bx-x^n).
