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.
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