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For $k\geq 2$, we derive an asymptotic formula for the number of zeros of theforms$\prod_{i=1}^{k}(x_{2i-1}^2+x_{2i}^2)+\prod_{i=1}^{k}(x_{2k+2i-1}^2+x_{2k+2i}^2)-x_{4k+1}^{2k}$and$x_1\prod_{i=1}^{k}(x_{2i}^2+x_{2i+1}^2)+x_{2k+2}\prod_{i=1}^{k}(x_{2k+2i+1}^2+x_{2k+2i+2}^2)-x_{4k+3}^{2k+1}$in the box $1\leq x_i\leq P$ using the circle method.

On a form of degree $d$ in $2d+1$ variables ($d\geq 4$)