Repertoire Method Clarification Required ( Concrete Mathematics )
Solution 1:
Put $R_n=1$ (for all $n$; hence also $R_0$ and $R_{n-1}$ should be set equal to 1) in (2.7): $$ 1 = \alpha, \quad 1 = 1 + \beta + \gamma n. $$ The first equation tells us $\alpha$ right away, and the second equality holds for all $n$ iff $\beta=\gamma=0$.
Then put $R_n=n$ (hence $R_0=0$ and $R_{n-1}=n-1$) in (2.7): $$ 0 = \alpha, \quad n = (n-1)+\beta + \gamma n. $$ Here $\beta=1$ and $\gamma=0$ is required for the identity to hold for all $n$ (compare coefficients for the constant terms and for the $n$-terms separately).
Etc.