Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 7 / c / i

A particular solution of the linear recurrence is $-n-1$, while its homogeneous solution is $C{2}^n$. The initial value gives $C-1=1$, soSubstitution verifies $u_{n+1}-2u_n=n$, and the recurrence plus $u_0$ determines all later terms uniquely.