  An almost complete intersection ideal can be seen as a $d$-sequence ideal
with the minimal number of generators being one more than its height. In this
paper, we give exact formulas for the regularity of powers of graded almost
complete intersection ideals. We also present the minimal bigraded free
resolutions of Rees algebras associated with linear type ideals having one
generator more than their grade and study the properties of Cohen-Macaualyness,
Koszulness associated to their diagonals.
