To understand let see first where the Sequence Number (SQN is used)
Input to AKA algorithm at HSS and UE side while generating AUTN(UE/HSS), RES(UE)/XRES(HSS), KAsmi(UE/HSS).
At both HSS and UE side KAsme is generated and it is never shared between them. It is one important key parameter. So instead of KASME, UE and MME share KSI Asme which is key vector number so that based on this UE/MME can know which KASME is currently used.
As the range of KSIASME is also 3 bit (0-7), so guessing it's like an intercepted authentication vector which acts as fake authentication.
So an additional number HSS generated sequence number which is increased both at UE and network each time they authenticate successfully. Even this HSS generated SQN number is concealed in AUTN-HSS and it is shared with UE during authentication request message. So that UE can extract it first time and use it to generate AUTN-UE and from increases each time when authenticates.
As a conclusion this extra sequence number makes secure while generating keys at though someone used fake authentication vector.
Hope it is clear.
Source :- From GSM to LTE: An Introduction to Mobile Networks and Mobile Broadband
