Extend New Binary Sequence ?

[Paul D. Hanna]

Seqfans, 
      To start with the correct offset (=0), the PARI program 
should have been: 
 
A000123(n) = if(n<1, n==0, A000123(n\2) + A000123(n-1)) 
 
a(n) = if(n==0,1, A000123( (2^(n+1) + (-1)^n - 3)/6 ) ) 
 
I do not know if there is any faster way of programming this ... 
Perhaps I will find a matrix approach that will be quick? 
 
Thanks for any tips or tries in extending this sequence. 
    Paul 
 
On Fri, 31 Aug 2007 19:48:11 -0400 Paul D. Hanna <pauldhanna at juno.com>
writes:
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)) 
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