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<DIV>Seqfans, <BR> Could someone also extend the
following sequence. </DIV>
<DIV>It appears in an interesting tree structure that I am studying. </DIV>
<DIV>Definition: </DIV>
<DIV> </DIV>
<DIV>a(n) = A000123( A000975(n-1) ) for n>=1 with a(0)=1, <BR>where
A000123(n) = number of partitions of 2n into powers of 2 <BR>and A000975(n) =
n-th number without consecutive equal binary digits. </DIV>
<DIV> </DIV>
<DIV>The sequence begins:</DIV>
<DIV> </DIV>
<DIV>1,1,2,4,14,60,450,4964,95982,3037948,</DIV>
<DIV> </DIV>
<DIV>but I can get no further before my old PARI gets "deep recursion". </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>This is an equivalent definition using PARI:</DIV>
<DIV> </DIV>
<DIV>a(n) = if(n==0,1, A000123( (2^(n+2) - (-1)^n - 3)/6 ) ) </DIV>
<DIV> </DIV>
<DIV>where </DIV>
<DIV>A000123(n) = if(n<1, n==0, A000123(n\2) + A000123(n-1)) </DIV>
<DIV> </DIV>
<DIV>Thanks for any help, </DIV>
<DIV> Paul </DIV></BODY></HTML>