Can pseudo-rectangular equal-area map projection have equidistant parallels?

Among the six pseudo-rectangular Eckert projections, three are equal area and three have equally spaced latitudes. The equal area maps have parallels spaced to preserve area, I wonder if the same can be achieved by changing the shape of the meridians.

Is it possible for an equal area pseudo-rectangular map projection to be both equal area and have equally spaced latitudes?

If yes, what are some examples of projections that share all three properties (equal area, pseudo-rectangular, equally spaced parallels)?

• Sinusoidal is close to what you want I think, except maybe no cylindrical enough. – mkennedy Nov 14 '18 at 17:26
• @mkennedy It's pseudocylindrical as long as all lines of latitude are straight parallel horizontal lines. – gerrit Nov 14 '18 at 17:31
• Yes, the sinusoidal projection is pseudocylindrical, equal area and the parallels are equally spaced, so it fits with your description. – FSimardGIS Nov 15 '18 at 0:12 