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Sums Involving Fibonacci and Pell Numbers
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On sums of powers of terms in a linear recurrence.
(1.1) { Un = pUn−1 − Un−2 , U0 = 0, U1 = 1 , Vn = p Vn−1 − Vn−2 , V0 = 2, V1 = p , where p ≥ 2 is an integer. For p = 2 {Un} becomes the sequence of non-negative integers, and for this reason we mayExpand
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Certain classes of finite sums that involve generalized Fibonacci and Lucas numbers
was the inspiration for [2], in which analogous sums involving cubes of Fibonacci numbers were developed. In turn, [2] was the motivation for [5], [6], and [7]. In the present paper, where weExpand
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Sums of certain products of Fibonacci and Lucas numbers
In Section 2 we prove a theorem involving a sum of products of Fibonacci numbers, and in Section 3 we prove the corresponding theorem for the Lucas numbers. In Section 4 we present three additionalExpand
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Some analogs of the identity F 2 n + F 2 n+1 = F 2n+1
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Analogues of Jacobi's Two-Square Theorem: An Informal Account
  • R. Melham
  • Computer Science, Mathematics
  • Integers
  • 2010
TLDR
We give numerous identities, each of which yields an analogue of Jacobi's two-square theorem, which involve polygonal numbers. Expand
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Finite Reciprocal Sums Involving Summands that are Balanced Products of Generalized Fibonacci Numbers
  • R. Melham
  • Mathematics, Computer Science
  • J. Integer Seq.
  • 12 May 2014
TLDR
In this paper we find closed forms, in terms of rational numbers, for certain finite sums involving generalized Fibonacci and Lucas numbers. Expand
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A GENERALIZATION OF THE CATALAN IDENTITY AND SOME CONSEQUENCES
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Reciprocal Series of Squares of Fibonacci Related Sequences with Subscripts in Arithmetic Progression
  • R. Melham
  • Mathematics, Computer Science
  • J. Integer Seq.
  • 2015
TLDR
We present closed forms for Fibonacci related reciprocal sums, both finite and infinite, in which the denominator of the summand is a perfect square. Expand
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