  An infinite real sequence $\{a_n\}$ is called an invariant sequence of the
first (resp., second) kind if $a_n=\sum_{k=0}^n {n \choose k} (-1)^k a_k$
(resp., $a_n=\sum_{k=n}^{\infty} {k \choose n} (-1)^k a_k$). We review and
investigate invariant sequences of the first and second kinds, and study their
relationships using similarities of Pascal-type matrices and their eigenspaces.
