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An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences (1105.3399v1)
Published 15 May 2011 in math.GM
Abstract: 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.