Given a sequence x={(x_n)}_{n\in\N}, one associates with this sequence the new sequence .
(A x)_n=x_n-\frac{(\Delta x_n)^2}{\Delta^2 x_n}, or equivalently = x_{n+2} - \frac{(\Delta x_{n+1})^2}{\Delta^2 x_n} = x_{n+2} - \frac{(x_{n+2}-x_{n+1})^2}{(x_{n+2}-x_{n+1})-(x_{n+1}-x_{n})} .