Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2))+ f(ceiling(n/2)) + g(n): theory and applications

Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2))+ f(ceiling(n/2)) + g(n): theory and applications, submitted for publication (December, 2016) pdf (1.8M, 49 pages, 46 figures)