Geodesic
New Ramanujan-type formulas and quasi-Fibonacci numbers of order 7
Journal of integer sequences, Tome 10 (2007) no. 5
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.
Classification : 11B83, 11A07, 39A10
Keywords: Ramanujan's formulas, Fibonacci numbers, primitive roots of unity, recurrence relation 
@article{JIS_2007__10_5_a2,
     author = {Witu{\l}a,  Roman and S{\l}ota,  Damian},
     title = {New {Ramanujan-type} formulas and {quasi-Fibonacci} numbers of order 7},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {5},
     zbl = {1140.11317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_5_a2/}
}
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Wituła,  Roman; Słota,  Damian. New Ramanujan-type formulas and quasi-Fibonacci numbers of order 7. Journal of integer sequences, Tome 10 (2007) no. 5. http://geodesic.mathdoc.fr/item/JIS_2007__10_5_a2/