[c#] IEnumerable<object> a = new IEnumerable<object>(); Can I do this?

Since you now specified you want to add to it, what you want isn't a simple IEnumerable<T> but at least an ICollection<T>. I recommend simply using a List<T> like this:

List<object> myList=new List<object>();
myList.Add(1);
myList.Add(2);
myList.Add(3);

You can use myList everywhere an IEnumerable<object> is expected, since List<object> implements IEnumerable<object>.

(old answer before clarification)

You can't create an instance of IEnumerable<T> since it's a normal interface(It's sometimes possible to specify a default implementation, but that's usually used only with COM).

So what you really want is instantiate a class that implements the interface IEnumerable<T>. The behavior varies depending on which class you choose.

For an empty sequence use:

IEnumerable<object> e0=Enumerable.Empty<object>();

For an non empty enumerable you can use some collection that implements IEnumerable<T>. Common choices are the array T[], List<T> or if you want immutability ReadOnlyCollection<T>.

IEnumerable<object> e1=new object[]{1,2,3};
IEnumerable<object> e2=new List<object>(){1,2,3};
IEnumerable<object> e3=new ReadOnlyCollection(new object[]{1,2,3});

Another common way to implement IEnumerable<T> is the iterator feature introduced in C# 3:

IEnumerable<object> MyIterator()
{
  yield return 1;
  yield return 2;
  yield return 3;
}

IEnumerable<object> e4=MyIterator();