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Several Generating Functions for SecondOrder Recurrence Sequences
"... Carlitz and Riordan began a study on closed form of generating functions for powers of secondorder recurrence sequences. This investigation was completed by Stănică. In this paper we consider exponential and other types of generating functions for such sequences. Moreover, an extensive table of gen ..."
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Carlitz and Riordan began a study on closed form of generating functions for powers of secondorder recurrence sequences. This investigation was completed by Stănică. In this paper we consider exponential and other types of generating functions for such sequences. Moreover, an extensive table
RECIPROCAL SUMS OF SECONDORDER RECURRENT SEQUENCES
, 1999
"... Let Z and IR (C) denote the ring of the integers and the field of real (complex) numbers, respectively. For a field F, we put i 7 * = F\{0}. Fix A GC and B G C*, and let X(A, B) consist of all those secondorder recurrent sequences {wn}neZ of complex numbers satisfying the recursion: w ..."
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Cited by 3 (0 self)
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Let Z and IR (C) denote the ring of the integers and the field of real (complex) numbers, respectively. For a field F, we put i 7 * = F\{0}. Fix A GC and B G C*, and let X(A, B) consist of all those secondorder recurrent sequences {wn}neZ of complex numbers satisfying the recursion: w
RECIPROCAL SUMS OF SECOND ORDER RECURRENT SEQUENCES
 FIBONACCI QUART. 39(2001), NO. 3, 214–220.
, 2001
"... Let Z and R (C) denote the ring of the integers and the field of real (complex) numbers respectively. For a field F we put F ∗ = F \ {0}. Fix A ∈ C and B ∈ C ∗, and let L(A, B) consist of all those second order recurrent sequences {wn}n∈Z of complex numbers satisfying the recursion: ..."
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Let Z and R (C) denote the ring of the integers and the field of real (complex) numbers respectively. For a field F we put F ∗ = F \ {0}. Fix A ∈ C and B ∈ C ∗, and let L(A, B) consist of all those second order recurrent sequences {wn}n∈Z of complex numbers satisfying the recursion:
THE EXISTENCE OF SPECIAL MULTIPLIERS OF SECONDORDER RECURRENCE SEQUENCES
, 2001
"... One approach to the study of the distributions of residues of secondorder recurrence sequences (wn) modulo powers of a prime p is to identify and examine subsequences w % = wn+tmj that are themselves firstorder recurrence sequences. In particular, the restricted period, h = h(p r), and the multip ..."
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One approach to the study of the distributions of residues of secondorder recurrence sequences (wn) modulo powers of a prime p is to identify and examine subsequences w % = wn+tmj that are themselves firstorder recurrence sequences. In particular, the restricted period, h = h(p r
PARTIAL SUMS FOR SECONDORDER RECURRENCE SEQUENCES
, 1993
"... Motivation for this paper comes from a short article [4] in which some relations between a generalized Fibonacci sequence and the sequence of its partial sums were investigated. An opportunity was clearly provided for a deeper exploration of this theme. Accordingly, the purpose of this paper is (a) ..."
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Cited by 1 (0 self)
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Motivation for this paper comes from a short article [4] in which some relations between a generalized Fibonacci sequence and the sequence of its partial sums were investigated. An opportunity was clearly provided for a deeper exploration of this theme. Accordingly, the purpose of this paper is (a
A POWER IDENTITY FOR SECONDORDER RECURRENT SEQUENCES
"... The following hold for all integers n and k: ..."
GENERATING FUNCTIONS FOR POWERS OF CERTAIN SECONDORDER RECURRENCE SEQUENCES
"... Let u(n) and v(n) be two sequences of numbers defined by n+l _ n+1 r (1) u(n) = ± 2 _ , n = 0, 1,2, ••• ..."
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Cited by 3 (0 self)
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Let u(n) and v(n) be two sequences of numbers defined by n+l _ n+1 r (1) u(n) = ± 2 _ , n = 0, 1,2, •••
Generating functions, weighted and nonweighted sums for powers of secondorder recurrence sequences
, 2000
"... In this paper we find closed forms of the generating function U r nx n, for powers of any nondegenerate secondorder recurrence sequence, Un+1 = aUn+bUn−1, a 2 +4b ̸ = 0, completing a study began by Carlitz [1] and Riordan [4] in 1962. Moreover, we generalize a theorem of Horadam [3] on partial sum ..."
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Cited by 6 (1 self)
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In this paper we find closed forms of the generating function U r nx n, for powers of any nondegenerate secondorder recurrence sequence, Un+1 = aUn+bUn−1, a 2 +4b ̸ = 0, completing a study began by Carlitz [1] and Riordan [4] in 1962. Moreover, we generalize a theorem of Horadam [3] on partial
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order differenti ..."
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Cited by 578 (6 self)
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We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order
Mining Sequential Patterns: Generalizations and Performance Improvements
 RESEARCH REPORT RJ 9994, IBM ALMADEN RESEARCH
, 1995
"... The problem of mining sequential patterns was recently introduced in [3]. We are given a database of sequences, where each sequence is a list of transactions ordered by transactiontime, and each transaction is a set of items. The problem is to discover all sequential patterns with a userspecified ..."
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Cited by 759 (5 self)
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The problem of mining sequential patterns was recently introduced in [3]. We are given a database of sequences, where each sequence is a list of transactions ordered by transactiontime, and each transaction is a set of items. The problem is to discover all sequential patterns with a user
Results 1  10
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4,376