  The asymptotics of the "strip" sums $S_\ell^{(\al)}(n)$ and of their $d$-sums
generalizations $T_{d,ds}^{(\al)}(dm)$ (see Definition~\ref{definition1}) were
calculated in~\cite{regev}. It was recently noticed that when $d>1$ there is a
certain confusion about the relevant notations in~\cite{regev}, and the
constant in the asymptotics of these $d$-sums $T_{d,ds}^{(\al)}(dm)$ seems to
be off by a certain factor. Based on the techniques of~\cite{regev} we again
calculate the asymptotics of the $d$-sums $T_{d,ds}^{(\al)}(dm)$. We do it here
carefully and with complete details. This leads to Theorem~\ref{d.sum222}
below, which replaces Corollary 4.4 of~\cite{regev} in the cases $d>1$.
