U 0 ( P , Q ) = 0 , U 1 ( P , Q ) = 1 , U n ( P , Q ) = P ⋅ U n − 1 ( P , Q ) − Q ⋅ U n − 2 ( P , Q ) ∀ n > 1 {\displaystyle {\begin{aligned}U_{0}(P,Q)&=0,\\U_{1}(P,Q)&=1,\\U_{n}(P,Q)&=P\cdot U_{n-1}(P,Q)-Q\cdot U_{n-2}(P,Q)\ \forall \ n>1\end{aligned}}}
V 0 ( P , Q ) = 2 , V 1 ( P , Q ) = P , V n ( P , Q ) = P ⋅ V n − 1 ( P , Q ) − Q ⋅ V n − 2 ( P , Q ) ∀ n > 1 {\displaystyle {\begin{aligned}V_{0}(P,Q)&=2,\\V_{1}(P,Q)&=P,\\V_{n}(P,Q)&=P\cdot V_{n-1}(P,Q)-Q\cdot V_{n-2}(P,Q)\ \forall \ n>1\end{aligned}}}
n U n ( P , Q ) V n ( P , Q ) 0 0 2 1 1 P 2 P P 2 − 2 Q 3 P 2 − Q P 3 − 3 P Q 4 P 3 − 2 P Q P 4 − 4 P 2 Q + 2 Q 2 5 P 4 − 3 P 2 Q + Q 2 P 5 − 5 P 3 Q + 5 P Q 2 6 P 5 − 4 P 3 Q + 3 P Q 2 P 6 − 6 P 4 Q + 9 P 2 Q 2 − 2 Q 3 {\displaystyle {\begin{array}{r|l|l}n&U_{n}(P,Q)&V_{n}(P,Q)\\\hline 0&0&2\\1&1&P\\2&P&{P}^{2}-2Q\\3&{P}^{2}-Q&{P}^{3}-3PQ\\4&{P}^{3}-2PQ&{P}^{4}-4{P}^{2}Q+2{Q}^{2}\\5&{P}^{4}-3{P}^{2}Q+{Q}^{2}&{P}^{5}-5{P}^{3}Q+5P{Q}^{2}\\6&{P}^{5}-4{P}^{3}Q+3P{Q}^{2}&{P}^{6}-6{P}^{4}Q+9{P}^{2}{Q}^{2}-2{Q}^{3}\end{array}}}
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