@article{oai:teapot.lib.ocha.ac.jp:00034612,
 author = {Hosoya, haruo and ホソヤ, ハルオ},
 issue = {2},
 journal = {お茶の水女子大學自然科學報告},
 month = {Feb},
 note = {application/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.},
 pages = {11--20},
 title = {Continuant, caterpillar, and topological index Z. II. Novel identities involving Fibonacci, Lucas, and generalized Fibonacci numbers},
 volume = {58},
 year = {2008}
}