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In this article we construct a family of domains $\Omega \subset\mathbb{R}^2$ with infinite volume such that the Dirichlet Laplacian $\Delta^D$has purely discrete spectrum and give precise spectral asymptotics for theeigenvalue counting function in terms of the geometry of $\Omega$. Thisgeneralizes the well-known asymptotic formula of Hermann Weyl to this class ofinfinite volume domains. The construction is elementary, uses only thebracketing technique invented by Weyl himself and it is extendable to arbitrarydimensions.

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