Consider an=an−1+an−2+1a_n = a_{n-1} + a_{n-2} + 1an=an−1+an−2+1. What is the particular solution an(p)a_n^{(p)}an(p) form?
an(p)=Aa_n^{(p)} = Aan(p)=A
an(p)=Ana_n^{(p)} = Anan(p)=An
an(p)=An+Ba_n^{(p)} = An + Ban(p)=An+B
an(p)=A(−1)na_n^{(p)} = A(-1)^nan(p)=A(−1)n