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<DIV>Seqfans,</DIV>
<DIV> There is a conflict in o.g.f.s for
sequence A000621:</DIV>
<DIV><A
href="http://www.research.att.com/projects/OEIS?Anum=A000621">http://www.research.att.com/projects/OEIS?Anum=A000621</A></DIV>
<DIV> </DIV>
<DIV>They are given as: </DIV>
<DIV>(1) G.f.: A(x)
=(1-x^2-x^8-x^4+x^10)/((x-1)*(x^9+2*x^8+x^7+x^6+x^5+2*x^4+x^3+x^2-1));</DIV>
<DIV> </DIV>
<DIV>(2) G.f.: A(x) = 1/1 - x/1 - x^2/1 - x^4/1 -...- x^(2^k)/1-...
(continued fraction); </DIV>
<DIV>or equivalently: </DIV>
<DIV>G.f. satisfies: A(x) = 1/(1 - x*A(x^2)).</DIV>
<DIV> </DIV>
<DIV>Formula (1) does NOT agree with the initial terms
given, whereas formula (2) does. </DIV>
<DIV> </DIV>
<DIV>Does someone have access to the references (see below) to
determine what is the correct g.f.? </DIV>
<DIV> </DIV>
<DIV>Thanks,</DIV>
<DIV> Paul</DIV>
<DIV> </DIV>
<DIV><STRONG>References: </STRONG></DIV>
<DIV>C. M. Blair and H. R. Henze, The number of stereoisomeric
and<BR><STRONG>
</STRONG> non-stereoisomeric mono-substitution products of the
paraffins,
J.<BR><STRONG>
</STRONG> Amer. Chem. Soc., 54 (1932),
1098-1105.<BR><STRONG> </STRONG></DIV>
<DIV>G. Polya, Algebraische Berechnung der Anzahl der Isomeren
einiger<BR><STRONG>
</STRONG> organischer Verbindungen, Zeit. f. Kristall., 93 (1936),
415-443;<BR><STRONG>
</STRONG> "q" on page 441.<BR> </DIV></BODY></HTML>