A000621 G.F.: Conflicting Formulas

[Alexandre Wajnberg]

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...).
 From this point of view, the seq, keeping its name, should begin with the
second term and offset 2.

Alexandre


De : "Paul D. Hanna" <pauldhanna at juno.com>
Date : Wed, 30 Nov 2005 23:39:21 -0500
À : <seqfan at ext.jussieu.fr>
Objet : A000621 G.F.: Conflicting Formulas

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


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20051201/dab0da3a/attachment-0001.htm>