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On the Partition of Horadam ' S Generalized Sequences into Generalized Fibonacci and Generalized Lucas Sequences
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hilton, Anthony J. W. |
| Copyright Year | 2010 |
| Abstract | which are not also first-order sequences; i.e., they do not satisfy Wn = cWn„7 fyn) for some c. In Horadam's papers ( [3 ] , [4 ] , [5 ] , [6]) our Wn is denoted by Wn(a,b;p,-q). In this paper we show that oo can be partitioned naturally into a set F of generalized Fibonacci sequences and a set L of generalized Lucas sequences; to each F e F there corresponds one L e L and vice-versa. We also indicate how very many of the well-known identities may be generalized in a simple way. 2. THE PARTITION OF oo(p,q) If a,(l are the roots of x -px -q = 0, d= +\/p + 4q then the following relationships are true: |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.mathstat.dal.ca/FQ/Scanned/12-4/hilton.pdf |
| Alternate Webpage(s) | http://www.fq.math.ca/Scanned/12-4/hilton.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
