Anindependentmethodforpaper[10]ispresented.WeightedlatticepathsareemumeratedbycountingfunctionwhichisanaturalextensionofGaussianmultinomialcoefficientinthecaseofunrestrictedpaths.Convolutionsforpathcountsareinvestigated.whichyieldssomeVandermonde-typeidentitiesformultinomialandq-multinomialcoefficients.