Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 2 / 2B / Solution

The characteristic polynomial of the linear recurrence relation isThe repeated-root rule therefore givesThe condition $x_0=0$ gives $A=0$. The other two conditions giveso $B+C=2$ and $B+2C=3$. Thus $B=C=1$, and

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