Count Valid Sequences

Problem Overview

• Count the number of valid sub-sequences of consecutive numbers from 1 to n that avoid all forbidden pairs.
• Input: integer n and a list of forbidden number pairs; Output: the count of valid sequences; sequences can be any length but must be contiguous in value.
• Real-world context: selecting runs of items while preventing incompatible pairings (combinatorics/domain logic).
• From Openai interviews; a coding interview problem commonly used as an interview question.