A000621 G.F.: Conflicting Formulas

Paul D. Hanna pauldhanna at juno.com
Thu Dec 1 05:39:21 CET 2005


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/20051130/89f01664/attachment.htm>


More information about the SeqFan mailing list