1 1 3

$${\left(\langle V\rangle \right)}^2\langle VPVPV{P}^{3}V\rangle$$

$$-\langle VPV\rangle \langle VPVPV{P}^{2}V\rangle$$

3 2

$$\langle VPV\rangle \langle V\rangle \langle V{P}^{2}V{P}^{2}V\rangle$$

$$-{\left(\langle V\rangle \right)}^3\langle V{P}^{3}V{P}^{2}V\rangle$$

2 3

$$\langle VPV\rangle \langle V\rangle \langle V{P}^{2}V{P}^{2}V\rangle$$

$$-{\left(\langle V\rangle \right)}^3\langle V{P}^{2}V{P}^{3}V\rangle$$

4 1

$$-\langle V{P}^{2}VPV\rangle \left(\langle VPVPV\rangle -\langle V\rangle \langle V{P}^{2}V\rangle \right)$$

$$\langle V\rangle \langle VPV\rangle \langle V{P}^{3}VPV\rangle$$

$$\langle V\rangle \langle VPV\rangle \langle V{P}^{3}VPV\rangle$$

$$-{\left(\langle V\rangle \right)}^3\langle V{P}^{4}VPV\rangle$$

1 4

$$-\langle V{P}^{2}VPV\rangle \left(\langle VPVPV\rangle -\langle V\rangle \langle V{P}^{2}V\rangle \right)$$

$$\langle V\rangle \langle VPV\rangle \langle VPV{P}^{3}V\rangle$$

$$\langle V\rangle \langle VPV\rangle \langle VPV{P}^{3}V\rangle$$

$$-{\left(\langle V\rangle \right)}^3\langle VPV{P}^{4}V\rangle$$

5

$$-\Delta E_4\langle V{P}^{2}V\rangle$$

$$\Delta E_1\Delta E_3\langle V{P}^{3}V\rangle$$

$$\Delta E_2\Delta E_2\langle V{P}^{3}V\rangle$$

$$\Delta E_3\Delta E_1\langle V{P}^{3}V\rangle$$

$$-{\left(\Delta E_1\right)}^2\Delta E_2\langle V{P}^{4}V\rangle$$

$$-{\left(\Delta E_1\right)}^2\Delta E_2\langle V{P}^{4}V\rangle$$

$$-{\left(\Delta E_1\right)}^2\Delta E_2\langle V{P}^{4}V\rangle$$

$${\left(\Delta E_1\right)}^4\langle V{P}^{5}V\rangle$$

$$S_5=S_4+2S_1{S}_3+S_2^2+3S_1^2{S}_2+S_1^4=5+2\times 2+1+3+1=14$$

$$\begin{array}{c}{S}_6=S_1^5+4S_1^3{S}_2+3S_2^2{S}_1+3S_3{S}_1^2+2S_3{S}_2+2S_4{S}_1+S_5\\ =1+4+3+3\times 2+2\times 2+2\times 5+14=42\end{array}$$

$$\begin{array}{c}\Delta E_6=\langle VPVPVPVPVPV\rangle -\Delta E_1\langle V{P}^{2}VPVPVPV\rangle -\Delta E_1\langle VPV{P}^{2}VPVPV\rangle \\ -\Delta E_1\langle VPVPV{P}^{2}VPV\rangle -\Delta E_1\langle VPVPV{P}^{2}V\rangle +{\left(\Delta E_1\right)}^2\langle V{P}^{2}V{P}^{2}VPV\rangle \\ +{\left(\Delta E_1\right)}^2\langle V{P}^{2}VPV{P}^{2}V\rangle +{\left(\Delta E_1\right)}^2\langle VPV{P}^{2}V{P}^{2}V\rangle +{\left(\Delta E_1\right)}^2\langle V{P}^{3}VPVPV\rangle \\ -\Delta E_2\langle V{P}^{2}VPVPV\rangle +{\left(\Delta E_1\right)}^2\langle VPV{P}^{3}VPV\rangle -\Delta E_2\langle VPV{P}^{2}VPV\rangle \\ +{\left(\Delta E_1\right)}^2\langle VPVPV{P}^{3}V\rangle -\Delta E_2\langle VPVPV{P}^{2}V\rangle +\Delta E_1\Delta E_2\langle V{P}^{2}V{P}^{2}V\rangle \\ -{\left(\Delta E_1\right)}^3\langle V{P}^{3}V{P}^{2}V\rangle +\Delta E_1\Delta E_2\langle V{P}^{2}V{P}^{2}V\rangle -{\left(\Delta E_1\right)}^3\langle V{P}^{2}V{P}^{3}V\rangle \\ -\Delta E_3\langle V{P}^{2}VPV\rangle +2\Delta E_1\Delta E_2\langle V{P}^{3}VPV\rangle -{\left(\Delta E_1\right)}^3\langle V{P}^{4}VPV\rangle \\ -\Delta E_3\langle VPV{P}^{2}V\rangle +2\Delta E_1\Delta E_2\langle VPV{P}^{3}V\rangle -{\left(\Delta E_1\right)}^3\langle VPV{P}^{4}V\rangle \\ -\Delta E_4\langle V{P}^{2}V\rangle +2\Delta E_1\Delta E_3\langle V{P}^{3}V\rangle +{\left(\Delta E_2\right)}^2\langle V{P}^{3}V\rangle \\ -3{\left(\Delta E_1\right)}^2\Delta E_2\langle V{P}^{4}V\rangle +{\left(\Delta E_1\right)}^4\langle V{P}^{5}V\rangle \end{array}$$