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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.27 No.1
- 발행연도
- 2017.1
- 수록면
- 115 - 130 (16page)
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초록· 키워드
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The difference sequence ∆ = (∆a0, ∆a1, ∆a2, . . .)T of a sequence a = (a0, a1, a2, . . .)T is defined by ∆ai = ai+1 - ai for each i = 0, 1, 2, . . .. Let ∆ia = (∆ia0, ∆ia1, ∆ia2, . . .)T , i = 0, 1, 2, . . ., be the ith difference sequence defined inductively by ∆ia = ∆(∆-1a) where ∆0a = a. Let Ma = [mij ], (i, j = 0, 1, 2, . . .) denote the difference matrix of a whose ith row is the transpose of the ith difference sequence and let Ha denote an infinite Hankel matrix with aT as its first row. The entries in Ma satisfy the Γlaw defined by the recurrence relation mi,j+1 = mi+1,j+mij. In this paper, the Γ-law is applied to examine the recurrence relations of difference sequences of Fk,l and Lk,l, where Fk,l and Lk,l are (k, l)-Fibonacci and (k, l)-Lucas sequences, respectively, for positive real numbers k and l. Finally, we show that MFk,l = P-1HFk,l and MLk,l = P-1HLk,l , where P is the Pascal matrix.
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참고문헌 (11)
참고문헌 신청
R. A. Brualdi / 2004 / Introductory Combinatorics / Prentice-Hall
G. -S. Cheon / 2003 / Matrices determined by a re-currence relation among entries / Linear Algebra Appl 373:89~99
G. -S. Choi / 2005 / ( 1)-Invariant sequences and truncated Fibonacci sequences / Linear Algebra Appl 395:303~312
L. Comtet / 1974 / Advanced Combinatorics / Dordrechet
S. Falcon / 2007 / On the Fibonacci k-numbers / Chaos, Solitons & Fractals 32:1615~1624
G. -S. Cheon / 2003 / Matrices determined by a re-currence relation among entries / Linear Algebra Appl 373:89~99
G. -S. Choi / 2005 / ( 1)-Invariant sequences and truncated Fibonacci sequences / Linear Algebra Appl 395:303~312
L. Comtet / 1974 / Advanced Combinatorics / Dordrechet
S. Falcon / 2007 / On the Fibonacci k-numbers / Chaos, Solitons & Fractals 32:1615~1624
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