Only the recursions are given for each step, since the certificates are extremely long.
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Step 1.
Step 2.
![Rec[3,0] := N+(n+r+1)*(n+s+1)*(n+t+1)*(2*n-r-s-t+1)*(2*n-r-s-t+2)/(n+1-s)/(n+1-r)/(n+1-t)/(n+1)/(n+1-r-s-t)](images/example4.gif){kind=small}
![Rec[3,1] := R+(n-r)*(n+r+1)*(n-r-s-t)/(r+1)^2/(2*n-r-s-t)](images/example5.gif)
![Rec[3,2] := S+(n-s)*(n+s+1)*(n-r-s-t)/(s+1)^2/(2*n-r-s-t)](images/example6.gif)
![Rec[3,3] := T+(n-t)*(n+t+1)*(n-r-s-t)/(t+1)^2/(2*n-r-s-t)](images/example7.gif)
Step 3.
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Step 5.
![rec[2,0] := N-(s+1)^2*(r-3*n+s-1)*(s-n+r)*(3*r^2-8*r*n-8*r+6*s*r+6+12*n-8*s+6*n^2-8*s*n+3*s^2)*(n+r+1)/(-n+s)/(s+r-1-n)^2/(n+1)^2/(-n+s-1)/(-n-1+r)*S+(-5*r+3*n-5*s+84*s*r*n+24*s*r-32*s*n-32*r*n+12*s^2+...](images/example10.gif)
![rec[2,0] := N-(s+1)^2*(r-3*n+s-1)*(s-n+r)*(3*r^2-8*r*n-8*r+6*s*r+6+12*n-8*s+6*n^2-8*s*n+3*s^2)*(n+r+1)/(-n+s)/(s+r-1-n)^2/(n+1)^2/(-n+s-1)/(-n-1+r)*S+(-5*r+3*n-5*s+84*s*r*n+24*s*r-32*s*n-32*r*n+12*s^2+...](images/example11.gif){kind=small}
![rec[2,0] := N-(s+1)^2*(r-3*n+s-1)*(s-n+r)*(3*r^2-8*r*n-8*r+6*s*r+6+12*n-8*s+6*n^2-8*s*n+3*s^2)*(n+r+1)/(-n+s)/(s+r-1-n)^2/(n+1)^2/(-n+s-1)/(-n-1+r)*S+(-5*r+3*n-5*s+84*s*r*n+24*s*r-32*s*n-32*r*n+12*s^2+...](images/example12.gif){kind=small}
![rec[2,0] := N-(s+1)^2*(r-3*n+s-1)*(s-n+r)*(3*r^2-8*r*n-8*r+6*s*r+6+12*n-8*s+6*n^2-8*s*n+3*s^2)*(n+r+1)/(-n+s)/(s+r-1-n)^2/(n+1)^2/(-n+s-1)/(-n-1+r)*S+(-5*r+3*n-5*s+84*s*r*n+24*s*r-32*s*n-32*r*n+12*s^2+...](images/example13.gif){kind=small}
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![rec[2,1] := R-1/(n+s+1)/(-n+s)/(r+1)^2*(s+1)^2*(n+r+1)*(-n+r)*S](images/example14.gif)
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Step 6.
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Step 7.
Step 5.
![rec[1,0] := N-(r+1)^2*(10*r-20*n+102*r*n-140*n^2-15*r^2-13*r^3-300*n^3+44*r^4-260*n^4-28*r^2*n+252*r*n^2-193*r^3*n+223*r^2*n^2+118*r*n^3+10*r^6-36*r^5-80*n^5-81*r^5*n+253*r^4*n^2+232*r^4*n-552*r^3*n^2+...](images/example19.gif){kind=small}
![rec[1,0] := N-(r+1)^2*(10*r-20*n+102*r*n-140*n^2-15*r^2-13*r^3-300*n^3+44*r^4-260*n^4-28*r^2*n+252*r*n^2-193*r^3*n+223*r^2*n^2+118*r*n^3+10*r^6-36*r^5-80*n^5-81*r^5*n+253*r^4*n^2+232*r^4*n-552*r^3*n^2+...](images/example20.gif){kind=small}
![rec[1,0] := N-(r+1)^2*(10*r-20*n+102*r*n-140*n^2-15*r^2-13*r^3-300*n^3+44*r^4-260*n^4-28*r^2*n+252*r*n^2-193*r^3*n+223*r^2*n^2+118*r*n^3+10*r^6-36*r^5-80*n^5-81*r^5*n+253*r^4*n^2+232*r^4*n-552*r^3*n^2+...](images/example21.gif){kind=small}
![rec[1,0] := N-(r+1)^2*(10*r-20*n+102*r*n-140*n^2-15*r^2-13*r^3-300*n^3+44*r^4-260*n^4-28*r^2*n+252*r*n^2-193*r^3*n+223*r^2*n^2+118*r*n^3+10*r^6-36*r^5-80*n^5-81*r^5*n+253*r^4*n^2+232*r^4*n-552*r^3*n^2+...](images/example22.gif)
![rec[1,0] := N-(r+1)^2*(10*r-20*n+102*r*n-140*n^2-15*r^2-13*r^3-300*n^3+44*r^4-260*n^4-28*r^2*n+252*r*n^2-193*r^3*n+223*r^2*n^2+118*r*n^3+10*r^6-36*r^5-80*n^5-81*r^5*n+253*r^4*n^2+232*r^4*n-552*r^3*n^2+...](images/example23.gif){kind=small}
![rec[1,0] := N-(r+1)^2*(10*r-20*n+102*r*n-140*n^2-15*r^2-13*r^3-300*n^3+44*r^4-260*n^4-28*r^2*n+252*r*n^2-193*r^3*n+223*r^2*n^2+118*r*n^3+10*r^6-36*r^5-80*n^5-81*r^5*n+253*r^4*n^2+232*r^4*n-552*r^3*n^2+...](images/example24.gif){kind=small}
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Step 6.
Step 7.
Stop.