An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences

We present an integral representation of Kekulé numbers for $P_{2} (n)$ benzenoids. Related integrals of the form $\int_{-π}^π \frac{\cos(nx)}{\sin^{2}x +k} dx$ are evaluated. Conjectures relating double integrals of the form $\int_{0}^{m} \int_{-π}^π \frac{\cos (2nx)}{k+\sin^{2}x} dx dk$ to Smarandache sequences are presented.

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