0
votes
2answers
54 views

Using generation functions solve the following difference equation

Using generation functions solve the following difference equation $$ a_{n+1} - 3a_{n+2} + 2a_n = 7n ; n\geq0; a_0 = -1; a_1 = 3. $$
0
votes
1answer
72 views

algebraic expression for a counting function

consider a 2d "counting" function given by the $(x,y)$ points/pairs: (1,1), (2,2),(3,2), (4,3),(5,3),(6,3), (7,4),(8,4),(9,4),(10,4), (11,5),(12,5),(13,5),(14,5),(15,5), ... ie $x$ increments in ...
2
votes
2answers
163 views

Recurrence $A(n,x)=p(x)A(n-1,x-1)+q(x)A(n-1,x)$

What is the general approach to solving this recurrent equation given that $p(x)$ and $q(x)$ are not constant and do not depend on $n$ and $p(x)+q(x) \neq 1$. Please just give me some hints, don't ...