Quadratic sequence

A sequence whose terms are generated by a rule involving the square of the position; its second differences are constant.

A sequence whose nth term can be written in the form $an^2+bn+c$, where $a$, $b$ and $c$ are constants and $a\ne0$.

A sequence with a constant, non-zero second difference and an nth-term expression of the form $an^2+bn+c$, where $a\ne0$.

A sequence whose nth term can be written in the form $an^2+bn+c$, where $a$, $b$ and $c$ are constants and $a\ne0$.

A sequence whose first differences change by a constant, non-zero amount; its position-to-term rule is quadratic.