Lattice paths and nn-colour compositions

Extending the ‘walks’ of van Lint and Wilson, we introduce a new kind of weighted lattice paths and show that the number of lattice paths with weight ν+m-1(0⩽m⩽ν-1)ν+m-1(0⩽m⩽ν-1) equals the number of n  -colour compositions of νν. Two new binomial identities with their combinatorial meaning are also obtained.