  Years ago Zeev Rudnick defined the ${\lambda}$-Poisson generic sequences as
the infinite sequences of symbols in a finite alphabet where the number of
occurrences of long words in the initial segments follow the Poisson
distribution with parameter ${\lambda}$. Although almost all sequences, with
respect to the uniform measure, are Poisson generic, no explicit instance has
yet been given. In this note we give a construction of an explicit
${\lambda}$-Poisson generic sequence over any alphabet and any positive
${\lambda}$, except for the case of the two-symbol alphabet, in which it is
required that ${\lambda}$ be less than or equal to the natural logarithm of
$2$. Since ${\lambda}$-Poisson genericity implies Borel normality, the
constructed sequences are Borel normal. The same construction provides explicit
instances of Borel normal sequences that are not ${\lambda}$-Poisson generic.
