Automatically generate coupled equations from given conditions

[malusigumede]

I would like you to help me create a python code that will automatically generate equations from given conditions for the given function F.

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The function is given by:

F(n1,n2)=Ax(n1,n2)+Bx(n1+1,n2)+Cx(n1-1,n2)+Dx(n1,n2+1)+Ex(n1,n2-1)

for n1+n2<N (where 0<n1,n2)

and

F(n1,n2)=Ax(n1,n2)

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Example

For n1+n2<=2
F(0,0)=Ax(0,0)+Bx(1,0)+Dx(0,1)
F(1,0)=Ax(1,0)+Cx(0,0)+Bx(2,0)+Dx(1,1)
F(0,1)=Ax(0,1)+Ex(0,0)+Bx(1,1)+Dx(0,2)
F(1,1)=Ax(1,1)
F(0,2)=Ax(0,2)
F(2,0)=Ax(2,0)