Results 131 to 140 of about 47,656 (155)
The Global Wheat Full Semantic Organ Segmentation (GWFSS) Dataset
Wang Z+35 more
europepmc +1 more source
Incomplete balancing and lucas-balancing numbers [PDF]
The aim of this article is to establish some combinatorial expressions of balancing and Lucas-balancing numbers and investigate some of their properties.
Bijan Kumar Patel+3 more
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Factoriangular numbers in balancing and Lucas-balancing sequence
In this paper, we prove the nonexistence of factoriangular numbers in balancing and Lucas-balancing sequence.
S. G. Rayaguru+2 more
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Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers
In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers.
S. G. Rayaguru, G. K. Panda
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Diophantine equations concerning balancing and Lucas balancing numbers
In this paper, we consider the sequence of balancing and Lucas balancing numbers. The balancing numbers $${B_n}$$ are given by the recurrence
Pallab Kanti Dey, Sudhansu Sekhar Rout
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On the Properties of Lucas-Balancing Numbers by Matrix Method
Balancing numbers n and balancers r are originally dened as the solution of the Diophantine equation 1 + 2 + ... + (n - 1) = (n + 1) + (n + 2) + ... + (n + r). If n is a balancing number, then 8n^2 +1 is a perfect square. Further, If n is a balancing number then the positive square root of 8n^2 + 1 is called a Lucas-balancing number.
Prasanta Kumar Ray
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Balancing and Lucas-Balancing hybrid numbers and some identities
In this paper, we introduce Balancing and Lucas-Balancing hybrid numbers. We examine some identities of Balancing and Lucas-Balancing hybrid numbers. We give some basic definitions and properties related to them. In addition, we find Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, exponential generating
Mıne Uysal, Engın Özkan
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Exact Divisibility by Powers of the Balancing and Lucas-Balancing Numbers
Asim Patra+2 more
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Spinor algebra of k-balancing and k-Lucas-balancing numbers
In this paper, we introduce and study a spinor algebra of [Formula: see text]-balancing numbers referred to as the [Formula: see text]-balancing and [Formula: see text]-Lucas-balancing spinors. First, we give [Formula: see text]-balancing quaternions and their some algebraic properties.
Kalika Prasad+3 more
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