A sequence encountered by Euler.

[creigh at o2online.de]

The following appears to be interesting:

A052924(n) = A006190(n+1) - A006190(n) 
4*A052924(n)_0 =  9*A006190(n+1)_0 - A006497(n+1)_0 - 2*A003688(n+1)_1  

where "_" gives the offset. 

A052924, Comments: Euler encountered this sequence when finding the largest root 
of z^2-3z-1=0.

A006190 : Denominators of continued fraction convergents to (3+Sqrt[13])/2. 
-  Benoit Cloitre (abcloitre(AT)wanadoo.fr), Jun 14 2003


A006497(n)=2T(n,3i/2)(-i)^n with T(n,x) Chebyshev's polynomials of the
              first kind (see A053120), and i^2=-1. - Paul Barry
              (pbarry(AT)wit.ie), Nov 15 2003


The (unproven) relations were submitted today as commentary.

Sincerely, 
Creighton