Counting lattice path with Sage

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Quite newbie with Sage but I try to count very standard lattice path with steps (1,0) and (0,1) on a grin (0,0) to (m,n) for positive integers n and m. I want also put constraints like for example "not touching the main. diagonal".

I can program it but maybe there are Sage libraries that can help me?

Thanks for any suggestions Gianfranco