Deterministic key generation In a situation where it is required to generate n number of keys deterministically from a single piece of seed information can we assume that b breached number of keys, no matter what the quantity would not help an attacker discover the previous nor next key in the set without the original seed data?

My initial thought is that it wont be possible due to the generation of one provably secure key to another provably secure key wouldn't given an attacker leverage leverage. If someone can confirm my thoughts though (or how wrong I am) that would be brilliant. Thanks.
What you want is a key derivation function (KDF).  Here's a fairly thorough list of some standardized ones.

Ps. The suggestion given by user1852723 to use HMAC, with your "seed" as the key and a counter (or other non-repeating sequence) as the input, more or less corresponds to the "Counter mode KDF" construction described in NIST SP 800-108, with HMAC as the underlying PRF.