  We count the number of alignments of $N \ge 1$ sequences when match-up types
are from a specified set $S\subseteq \mathbb{N}^N$. Equivalently, we count the
number of nonnegative integer matrices whose rows sum to a given fixed vector
and each of whose columns lie in $S$. We provide a new asymptotic formula for
the case $S=\{(s_1,\ldots,s_N) \:|\: 1\le s_i\le 2\}$.
