Getting odd/even part of a sequence with LINQ

var projectsByCat = from p in Projects
                    group p by p.Category into g
                    orderby g.Count() descending
                    select new { Category = g.Key, Projects = g };

var oddCategories = projectsByCat.Where((cat, index) => index % 2 != 0);

var evenCategories = projectsByCat.Where((cat, index) => index % 2 == 0);

var oddCategories  = projectsByCat.ToList().Where((c,i) => i % 2 != 0);
var evenCategories = projectsByCat.ToList().Where((c,i) => i % 2 == 0);

var projectsByCat =
    (from p in Projects
    group p by p.Category into g
    orderby g.Count() descending
    select new { Category = g.Key, Projects = g }).ToList();

var oddCategories = projectsByCat.Where((cat, index) => index % 2 != 0);
var evenCategories = projectsByCat.Where((cat, index) => index % 2 == 0);