# Notation for multi-level hierarchical model

I'm having a hard time understanding how to write a multi-level hierarchical linear regression model in mathematical language. Suppose, for example, that our independent variable is x, our dependent variable is y, and that we have a 3 level hierarchy: C is nested inside B which is nested inside A. Also, suppose that we have a random-slopes model. How do we write this model? Here's what I have so far:

$Y_{iabc} = \beta_0 + \beta_1 C_{abc} x_i + \epsilon_{iabc}$

$C_{abc} = \beta_{10} + \beta_{11} B_{ab} + \delta_{abc}$

$B_{ab} = \beta_{110} + \beta_{111} A_a + \gamma_{ab}$

$A_a \sim N(0, \xi^2)$