Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.6

New Ramanujan-Type Formulas and Quasi-Fibonacci Numbers of Order 7

Roman Wituła and Damian Słota
Institute of Mathematics
Silesian University of Technology
Kaszubska 23
Gliwice 44-100
Poland

Abstract: We give applications of the quasi-Fibonacci numbers of order 7, the so-called sine-Fibonacci numbers of order 7, and many other new kinds of recurrent sequences to the decompositions of some polynomials. We also present the characteristic equations, generating functions and some properties of all these sequences. Finally, some new Ramanujan-type formulas are generated.

(Concerned with sequences A001607 A002249 A079309 A094648 A110512 and A115146 .)

Received April 19 2007; revised version received May 17 2007. Published in Journal of Integer Sequences, June 4 2007.