已知 Sn{S}_{n}Sn 是数列 {an}\left\{ {a}_{n}\right\}{an} 的前 nnn 项和,且 a1=a2=1,an=2an−1+3an−2 (n≥3){a}_{1} = {a}_{2} = 1,{a}_{n} = 2{a}_{n - 1} + 3{a}_{n - 2} \; \left( {n \geq 3}\right)a1=a2=1,an=2an−1+3an−2(n≥3) ，则下列结论正确的是（ ）A. 数列 {an−an+1}\left\{ {{a}_{n} - {a}_{n + 1}}\right\}{an−an+1} 为等比数列B. 数列 {an+1+2an}\left\{ {{a}_{n + 1} + 2{a}_{n}}\right\}{an+1+2an} 不为等比数列C. S40=14(320−1){S}_{40} = \frac{1}{4}\left( {{3}^{20} - 1}\right)S40=41(320−1)D. an=3n−1+(−1)n−12{a}_{n} = \frac{{3}^{n - 1} + {\left( -1\right) }^{n - 1}}{2}an=23n−1+(−1)n−1