Extend New Binary Sequence ?

[Paul D. Hanna]

Seqfans, 
     Could someone also extend the following sequence. 
It appears in an interesting tree structure that I am studying. 
Definition: 
 
a(n) = A000123( A000975(n-1) ) for n>=1 with a(0)=1, 
where A000123(n) = number of partitions of 2n into powers of 2 
and A000975(n) = n-th number without consecutive equal binary digits. 
 
The sequence begins:

1,1,2,4,14,60,450,4964,95982,3037948,

but I can get no further before my old PARI gets "deep recursion". 
 

This is an equivalent definition using PARI:
 
a(n) = if(n==0,1, A000123( (2^(n+2) - (-1)^n - 3)/6 ) ) 
 
where 
A000123(n) = if(n<1, n==0, A000123(n\2) + A000123(n-1)) 
 
Thanks for any help, 
      Paul 
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