A sequence encountered by Euler.
creigh at o2online.de
creigh at o2online.de
Fri Nov 5 00:40:46 CET 2004
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
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