Partitions: Parts Occuring-In/Missing-From Sequence

[Leroy Quet]

Are these sequences already in the EIS, perhaps under a different name?

If they aren't, could someone please calculate/submit them?

1) a(0)=1. a(n) = number of partitions of n into parts, at least one of 
which occurs earlier in {a(k)}.

Sequence begins (I think): 1, 1, 1, 2, 4, 6, 10, 14,...


2) b(1) = 1. b(n) = number of partitions of n into parts, each part 
missing from the first (n-1) terms of {b(k)}.

Sequence begins  (I think): 1, 1, 1, 2, 1, 2, 2,...


3) c(1) = 1. c(n) = number of partitions of n into parts, at least one of 
which is missing from the first (n-1) terms of {c(k)}.

Sequence begins (I think): 1, 1, 2, 2, 4, 7, 8,...


thanks,
Leroy Quet