A multi-laminated HTS tape conductor has been recently developed for large coils. If the HTS tapes are simply laminated to form the conductor, the current distribution in the laminated tape conductor of the coil is imbalanced because of the differences among all tape inductances. Transposition of the tapes in the conductor is effective for homogeneous current distribution, but the tape may be damaged due to the lateral bending. The solenoid coil has enough space to transpose the tapes at both ends. However, a proposed theory so far requires a restriction in the number of coil layers for homogeneous current distribution in the laminated tape conductor. It is very important to analyze current distributions in the multi-laminated tape conductor for the solenoid coil with arbitrary layers. In this paper, we apply the Maxwell integral equation to the region contoured by adjacent laminated tapes to analyze the current distributions of the tapes in an infinite solenoid coil, and demonstrate that the flux across the region is conserved as long as the tapes are not saturated, and finally induce the fundamental equations as functions of coil construction parameters, such as layer radii, laminated tape spaces, and winding pitches. We use the fundamental equations for 2 and 4-layer coils to verify the homogeneous current distribution of the laminated tape conductor for an arbitrary layer number. Since the flux between the tapes in the inner layer of a 2-layer coil is contributed from the outer layers, the tape space in the outer layer must be larger than that in the inner layer because of the balance between the two fluxes. Moreover, we have developed an analysis method for a finite solenoid coil.