The purpose of this study is to determine the fine spectra of the operator for which the corresponding lower and upper triangular matrices A(r,s,t) and B(r,s,t) are on the sequence spaces c and ellp, where (0<p<1), respectively. Further, we obtain the approximate point spectrum, defect spectrum and compression spectrum on these spaces. Furthermore, we give the graphical representations of the spectrum of the triangular triple-band matrix over the sequence spaces c and ellp