Given:
$a_{m,0}=0,$
$0<q,r<p<1,$
$p+q+r=1,$
$D_0,D_1>0,$
and an integer $k > 0$, s.t. $k*q<1;$
does there exist an explicit form for the the following recurrence relation:
$a_{m,n} = p*a_{m,n-1} + q*a_{m,n+k} + r*a_{m+1,n} + D_0*m +D_1$?
If so, what is it?