[seqfan] Re: A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes

[Richard Mathar]

vj> From seqfan-bounces at list.seqfan.eu Thu Mar 12 16:24:22 2009
vj> From: "Vladeta Jovovic" <vladeta at eunet.yu>
vj> To: <seqfan at list.seqfan.eu>
vj> Subject: [seqfan] A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes
vj> ...
vj> There is  Eric Weisstein's recent seq. A158007:  number of simple connected noneulerian graphs on n nodes.
vj> Clearly  A158007(n) = A001349(n) - A003049(n).
vj> 
vj> Interestingly, it appears that Euler transform of  A158007(n) gives A007126(n+1).
vj> ...

If "E" is the Euler transform we have

A001349 -> E-> A000088

A003049 -> E-> A002854

So to show that 
A158007 -> E -> A007126

you can equivalently show that A000088+A002854=A007126.
My graph theoretical background is too weak to address that
question.

RJM