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