What is the most efficient way to find a sequence within a IEnumerable using LINQ
I want to be able to create an extension method which allows
The code you say you want to be able to use isn't LINQ, so I don't see why it need be implemented with LINQ.
This is essentially the same problem as substring searching (indeed, an enumeration where order is significant is a generalisation of "string").
Since computer science has considered this problem frequently for a long time, so you get to stand on the shoulders of giants.
Some reasonable starting points are:
http://en.wikipedia.org/wiki/Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm
http://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string_search_algorithm
http://en.wikipedia.org/wiki/Rabin-karp
Even just the pseudocode in the wikipedia articles is enough to port to C# quite easily. Look at the descriptions of performance in different cases and decide which cases are most likely to be encountered by your code.