%0 Journal Article
%T An Integral Representation of Kekul¨¦ Numbers, and Double Integrals Related to Smarandache Sequences
%A John M. Campbell
%J Mathematics
%D 2011
%I arXiv
%X We present an integral representation of Kekul\'{e} numbers for $P_{2} (n)$ benzenoids. Related integrals of the form $\int_{-\pi}^{\pi} \frac{\cos(nx)}{\sin^{2}x +k} dx$ are evaluated. Conjectures relating double integrals of the form $\int_{0}^{m} \int_{-\pi}^{\pi} \frac{\cos (2nx)}{k+\sin^{2}x} dx dk $ to Smarandache sequences are presented.
%U http://arxiv.org/abs/1105.3399v1