2021-08-02T15:22:38Zhttps://teapot.lib.ocha.ac.jp/oaioai:teapot.lib.ocha.ac.jp:000346122021-03-01T22:18:55ZContinuant, caterpillar, and topological index Z. II. Novel identities involving Fibonacci, Lucas, and generalized Fibonacci numbersHosoya, haruo70978ホソヤ, ハルオ70979400application/pdf紀要論文The three series of numbers, Fibonacci (Fn) Lucas, (Ln) and generalized Fibonacci (Gn) are defined to have the same recursive relation, un = u_<n-1>+u_<n-2*> By imposing the following set of initial conditions, f_0=f_1=1, L_1=1 and L_2=3, and G_1=a>0 and G2=b>0 with b>2a, a number of novel identities were found which systematically relate f_n, L_n, and G_n with each other. Further, graph-theoretical interpretation for these relations was obtained by the aid of the continuant, caterpillar graph, and topological index Z which was proposed and developed by the present author.departmental bulletin paperお茶の水女子大学2008-02application/pdfお茶の水女子大學自然科學報告2581120AN0003395800298190https://teapot.lib.ocha.ac.jp/record/34612/files/58-2p.11-20.pdfeng