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<TITLE>Re : A000621 G.F.: Conflicting Formulas</TITLE>
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I wonder also if the first term makes sense chemically speaking, because an alkane with zero atom of carbon is not any more an alkane (except if the X is itself an alkane, but then it becomes another term of the same sequence...).<BR>
From this point of view, the seq, keeping its name, should begin with the second term and offset 2.<BR>
<BR>
Alexandre<BR>
<BR>
<HR ALIGN=CENTER SIZE="3" WIDTH="95%"><B>De : </B>"Paul D. Hanna" <pauldhanna@juno.com><BR>
<B>Date : </B>Wed, 30 Nov 2005 23:39:21 -0500<BR>
<B>À : </B><seqfan@ext.jussieu.fr><BR>
<B>Objet : </B>A000621 G.F.: Conflicting Formulas<BR>
<BR>
Seqfans,<BR>
There is a conflict in o.g.f.s for sequence A000621:<BR>
<a href="http://www.research.att.com/projects/OEIS?Anum=A000621">http://www.research.att.com/projects/OEIS?Anum=A000621</a><BR>
<BR>
They are given as: <BR>
(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));<BR>
<BR>
(2) G.f.: A(x) = 1/1 - x/1 - x^2/1 - x^4/1 -...- x^(2^k)/1-... (continued fraction); <BR>
or equivalently: <BR>
G.f. satisfies: A(x) = 1/(1 - x*A(x^2)).<BR>
<BR>
Formula (1) does NOT agree with the initial terms given, whereas formula (2) does. <BR>
<BR>
Does someone have access to the references (see below) to determine what is the correct g.f.? <BR>
<BR>
Thanks,<BR>
Paul<BR>
<BR>
<B>References: <BR>
</B>C. M. Blair and H. R. Henze, The number of stereoisomeric and<BR>
<B> </B> non-stereoisomeric mono-substitution products of the paraffins, J.<BR>
<B> </B> Amer. Chem. Soc., 54 (1932), 1098-1105.<BR>
<B> <BR>
</B>G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger<BR>
<B> </B> organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443;<BR>
<B> </B> "q" on page 441.<BR>
<BR>
<BR>
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