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All paths have the same number of left right moves which is determined by the end point.
Like 3-1 has You could easily do a recursion which checks and decrements $l and $r.
Cheers Rolf
*) see Re: compute paths in Pascal's triangle (aka Tartaglia's one) (2 updates) for explanation In reply to Re: compute paths in Pascal's triangle (aka Tartaglia's one)
by LanX
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