def mom_111(self, idxi, idxj, idxk):
        """Backend moment for i, j, k == 1, 1, 1."""
        if (idxi, idxj, idxk) in self.hist:
            return self.hist[idxi, idxj, idxk]

        if idxi == idxk == 0 or idxi == idxj == 0:
            out = 0

        elif chaospy.bertran.add(idxi, idxk, self.dim) < idxj \
                or chaospy.bertran.add(idxi, idxj, self.dim) < idxk:
            out = 0

        elif chaospy.bertran.add(idxi, idxj, self.dim) == idxk:
            out = 1

        elif idxj == idxk == 0:
            out = self.dist.mom(chaospy.bertran.multi_index(idxi, self.dim))

        elif idxk == 0:
            out = self.mom_110(idxi, idxj, idxk)

        else:
            out = self.mom_recurse(idxi, idxj, idxk)

        self.hist[idxi, idxj, idxk] = out

        return out