[seqfan] extending A003241
Richard Mathar
mathar at strw.leidenuniv.nl
Wed Sep 28 14:46:40 CEST 2011
In an attempt to extend http://oeis.org/A003241, I took the generating
function of A003238, shifted by one index to generate the function P(n)
of Harary-Robinson, then used eq (37) by Harary-Robinson
R(x) = 2x+P^2(x)/x^2 + (1-x)*P(x)*[P(x^2)/x^2-1]/x
-[(P^2(x)-P(x^2))/(2x)+P(x^3)/x^2]
-[P^2(x^2)-P(x^4)]/(2x^3)
and got for R(x) the coefficients
1,1,2,2,8,15,24,45,71,106,168,247,345,503,700,934,...
This is not what Harary and Robinson put into table 1, column R_n,
which is -- I think-- reproduced in A003241.
Where is the error? Is this a typo in the paper, my misunderstanding
of annotations found in eqs (39)-(44), or a typo in my Maple program?
L := BFILETOLIST("b003238.txt") ;
P := add( op(i,L)*x^(i+1),i=1..120) ;
Px2 := subs(x=x^2,P) ;
Px3 := subs(x=x^3,P) ;
Px4 := subs(x=x^4,P) ;
R := 2*x+P^2/x^2+(1-x)*P/x*(Px2/x^2-1)-(P^2-Px2)/2/x -Px3/x^2-(Px2^2-Px4)/2/x^3 ;
taylor(R,x=0,40) ;
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