Question: I have never been good at solving recurrence relations. Part of the reason is that I have never found a book that is good at explaining the strategies for solving them; The books just give formulas for solving recurrence relations of specific forms.

So, what books do you recommend to learn how to solve recurrence relations?

Answer: 
Here I'd like to draw attention to *[The Concrete Tetrahedron](https://www.maa.org/press/maa-reviews/the-concrete-tetrahedron)* by M. Kauers and P. Paule. This book puts the focus on four strongly connected types of mathematical objects

* recurrences
* generating functions
* symbolic sums
* asymptotic estimations

and the interplay between them. The connections and structural properties of these four regions are analysed starting with polynomials as the most simple application and going step by step, i.e. chapter by chapter to more complex objects. The authors cover

* Polynomials
* *[C-finite Sequences](https://en.wikipedia.org/wiki/Constant-recursive_sequence)*
* *[Hypergeometric Series](https://en.wikipedia.org/wiki/Hypergeometric_function#The_hypergeometric_series)*
* *[Algebraic Functions](https://en.wikipedia.org/wiki/Algebraic_function)*
* *[Holonomic Sequences and Power Series](https://en.wikipedia.org/wiki/Holonomic_function)*

and in each of these chapters the four regions and their interplay is discussed.

Btw. the term **Concrete** in the title of the book is a reverence to *[Concrete Mathematics](https://www.csie.ntu.edu.tw/%7Er97002/temp/Concrete%20Mathematics%202e.pdf)*
by R. L. Graham, D. Knuth and O. Patashnik which is explicitly stated by the authors in section 1.6:

* The attribute concrete is a reference to the book "Concrete Mathematics" by Graham, Knuth, and Patashnik [24], where a comprehensive introduction to the subject is provided. Following the authors of that book, we understand concrete not in contrast to abstract, but as a blend of the two words con-tinuous and dis-crete, for it is both continuous and discrete mathematics that is applied when solving concrete problems.
RECURRENCE AND TOPOLOGY,
John M. Alongi,
Gail S. Nelson,
Graduate Studies in Mathematics,Volume 85,
American Mathematical Society.
Providence, Rhode Island.
Publication Year: 2007
ISBN-10: 0-8218-4234-X
ISBN-13: 978-0-8218-4234-8
[www.ams.org/bookpages/gsm-85](http://www.ams.org/bookpages/gsm-85)