  High-order harmonic generation (HHG) is investigated for H$_2^+$ and its
isotopomers under seven- and ten-cycle trapezoidal laser pulses at 800 nm
wavelength and $I$=4$\times 10^{14}$ W$/$cm$^2$ intensity. We solved
numerically full-dimensional electronic time-dependent Schr\"{o}dinger equation
with and without the Born-Oppenheimer approximation. We show that the HHG at
the falling edge of a trapezoidal laser pulse can result in redshift and
complexity on the total HHG spectrum which can be removed by considering
different laser pulse duration and nuclear motion not possible for sin$^2$ and
Gaussian laser pulses. We resolve the redshifts and complexities of the HHG
spectra into different electronic and vibrational states and their
interferences.
