Refined sum formulas for finite multiple zeta values of level two

In this paper, we establish two classes of refined sum formulas for finite multiple zeta values of level two, a variant of finite multiple zeta values recently introduced by M. Kaneko et al. One is an explicit formula for the sum of level-two finite multiple zeta values over indices in which one prescribed component is odd and all the remaining components are even. The other is an Ohno–Zagier type relation for level-two finite multiple zeta values, which gives a generating function for sums of fixed weight, depth and height in terms of depth-one values. As applications, we derive sum formulas for fixed weight and depth and for several special heights.