Hi, i would like to create a function , or a sum that is bivariate and the sum of two variables give me a specific number.
For example, lets say I have a function f[x,y], where x,y integers and >0.
I need to create a function, lets say it G, where
if z==0 then G[0] = f[0,0]
if z==1 then G[1]= f[1,0] + f[0,1]
if z==2 then G[2]= f[2,0]+f[0,2]+f[1,1]
...
if z==k then G[k]= f[k,0]+ f[k-1,1]+f[k-2,2]+......+f[2,k-2]+f[1,k-1]+f[0,k]
I was trying to make a double sum like Sum[f[i,j],{i,0,k},{j,0,k}]
apparently this is not correct, but that would be a convinient solution for my problem, but i have trouble finding indeces i,j.
Does anyone have any idea?
Thank you in advance.