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Morgado Identity

An identity satisfied by $w$ Generalized Fibonacci Numbers:

$4w_nw_{n+1}w_{n+2}w_{n+4}w_{n+5}w_{n+6}+e^2q^{2n}(w_nU_4U_5-w_{n+1}U_2U_6-w_nU_1U_8)^2$
$ = (w_{n+1}w_{n+2}w_{n+6}+w_nw_{n+4}w_{n+5})^2,\quad$ (1)
where

$\displaystyle e$ $\textstyle \equiv$ $\displaystyle pab-qa^2-b^2$ (2)
$\displaystyle U_n$ $\textstyle \equiv$ $\displaystyle w_n(0,1; p,q).$ (3)

See also Generalized Fibonacci Number


References

Morgado, J. ``Note on Some Results of A. F. Horadam and A. G. Shannon Concerning a Catalan's Identity on Fibonacci Numbers.'' Portugaliae Math. 44, 243-252, 1987.




© 1996-9 Eric W. Weisstein
1999-05-26